(In this post I’m going to consider the relationship between a consulting detective and the police, from the perspective of writing about them. Nothing in this post is meant as literary criticism of any examples which are considered.)
In most murder mysteries, the police are investigating the murder, which presents the writer the problem of what the relationship between the police and the detective will be. Authors have chosen all over the spectrum, from the police seeking out the help of the consulting detective to the police actively trying to deter the consulting detective. (This has even been true of murder mysteries in which the main detective is the police! In that case it takes the form of his superiors respecting him to his superiors assigning him elsewhere and forbidding him from investigating.)
Authors will also change things up. In The Cadfael Chronicles stories, Sheriff Gilbert Prestcote is mildly antagonistic to Cadfael, whereas his successor Hugh Beringar is a good friend of Cadfael’s and though competent himself, values Cadfael’s opinion highly (it would probably be more accurate to say because he is competent himself). In Murder, She Wrote the different locations for the murder allowed them to try out the entire spectrum, though for some reason the Cabot Cove sheriffs tended to be more on the skeptical side. Perhaps the actors in question were just better at scowling than they were at smiling. Sherlock Holmes and Hercule Poirot had excellent reputations and friends in high places which tended to make the police friendly for them. Dorothy L. Sayers solved this with Lord Peter Wimsey by making the police deferential to his title of nobility. Philo Vance was a long-time friend of the district attorney. That’s only a small sampling and it’s all over the place. Clearly anything will work, but it leaves the question of which is best?
Of course, to even ask the question that way is to highlight that the real question is what sort of stories do the points on the curve allow you to tell? It’s always easiest to start at the extremes. If the police are highly antagonistic to the detective—e.g. the detective is the prime suspect and there is an arrest warrant out for the detective—this tends to be more conducive to stories with a lot of action/suspense. In the examples I can think of (The Fugitive and Minority Report come to mind) most of the focus is on whether the detective will be caught before he can prove he didn’t do it. This also tends to raise the stakes by having an innocent person in danger of being punished for a crime they didn’t commit.
On the other end of the spectrum, the police enthusiastically ask for the detective’s help and will do anything the detectives tells them to. Some episodes of Murder, She Wrote come to mind. Some of the Lord Peter Wimsey stories come close to it as well. Come to think of it, so do a few of the Sherlock Holmes stories. The stakes tend to be lower—though not always; Lord Peter had police cooperation in Strong Poison but Harriet Vane was on trial for a crime she didn’t commit—and most of the action tends to be the actual investigation. This tends to open up more space for theorizing and collaboration. Unless it’s an ongoing murder story—where live characters keep turning into dead bodies—these stories are more likely to have a slower pace and focus more on dialog than action.
(It is of course possible to change locations on this spectrum throughout the story. A detective, once cleared, can be welcomed by the police. A detective who had full access can turn into a suspect (this is especially easy to do if there are ongoing murders). A story can start more in the middle and once the detective proves useful, they can become more welcome. Etc.)
I think that my own preference is for the friendlier side of the spectrum. I enjoy collaboration more than I do conflict. Conflict can certainly be interesting, and is often easier to make interesting than collaboration, but I think that collaboration done well has a greater potential for interest. Individuals are interesting, but people are more themselves in community. Of course, it must be a true community. False community obliterates the individual for the sake of the group, while real community brings each individual to the fullness of themselves, respecting each one’s unique virtues. (As a technical note, I mean their unique natural virtues. Moral virtues are—in an ideal world, at least—not distinct between people. All men should be perfectly honest, but each one’s identical perfect honesty will have a different natural content because they know different things.)
A friendly relationship between the police and a consulting detective is not easy to pull off, however, especially if one is striving for realism. There is something of a natural antagonism between a consulting detective and the police, and further there is a natural reticence the police will have in sharing information which is not public. Still, the police will certainly consult outside experts, and police departments have been known to consult psychics for help. In The Dean Died Over Winter Break the relationship was probably more neutral than welcoming, but the police were reasonably friendly. Still, the information mostly flowed from the detectives to the police, and not the other way around. In the circumstance, it seemed the most natural thing.
One of the more plausible ways of insinuating the consulting detective with the police involves the police being short on resources. Resource shortages have a number of effects on people, most of them tending to increase flexibility. People with too few resources tend to see the upsides of shortcuts and other sorts of flexibility more clearly than do people with enough resources to get everything done. They tend to be less worried about possible downsides, because the downsides compare to the downside of simply not getting their work done. Moreover, the people who are responsible for the short-staffing cannot credibly threaten to replace the overworked person with someone else. Finding people willing to be overworked is not easy, and in any event finding new people for a job is both difficult and expensive. Worse for the person responsible for the short-staffing, since overworked people often make mistakes and don’t get everything done, disciplinary issues will have come up before, and the overworked person will probably have gotten used to the toothlessness of any threats made. Thus by the time the consulting detective comes around, offering to take some of the work off of the overworked police detective’s shoulders, the upside will be all the more obvious while the downsides will already be known to be minimal. And since the worst case is that the overworked person finally stops being overworked, the downsides will seem especially minimal.
Also viable for making police collaboration with the consulting detective plausible is for the forensic evidence to be scant. Really it’s not just the forensic evidence, but all of the evidence in which the police are the best at obtaining: cell phone records, bank records, the sort of evidence for which warrants are generally attainable, etc. If the police don’t really know anything of value, they have very little to lose in a relationship with the consulting detective. The flip side of the fairly impressive powers to subpoena phone records, etc. is that they are bound by rules which private citizens are not. Moreover the police are bound to enforce all rules, though of course in practice they don’t always do so, but this makes the police scary since in the modern age virtually everyone is guilty of some crime or other. We have so many laws its impossible to know what they all are, and some of them run counter to common sense (especially copyright laws). Children and pets offer all sorts of judgement-based ways in which the police could make a person’s life miserable even if they haven’t technically broken any laws; a great many people are rightfully wary about anyone as powerful as the police. None of this applies to a consulting detective, who has no power and is therefore relatively safe. Further, with no superiors to whom a person can complain, a consulting detective is in a less vulnerable position if they take liberties with people who have valuable information (providing those liberties are within the law).
There are of course plenty of other ways for a consulting detective to get along with the police. Friends and relatives on the police force have been used innumerable times. If a consulting detective is likable a police detective might simply take a liking to them. Having a mutual friend and helping the consulting detective for the sake of the friend is certainly possible, as is there being someone in authority over the police who wants the consulting detective working on the case. My memory might be deceiving me, but I think I’ve even seen it work for the consulting detective to—in effect—blackmail the police detective into sharing information. Since precedent is a powerful thing, I’ve also seen it done to bootstrap the consulting detective into a relationship with the police by some means which would only work once—a relative of the deceased having (politically expensive to use) power over the police, for example—which leaves the police eager to work with the detective again. I think that the choice of these techniques, if one wants to go this way, is going to depend on the detectives. In the case of my detectives—The Franciscan Brothers of Investigation—the choice varies with who it was that called the brothers in. In The Dean Died Over Winter Break, since it was the university president, this acted as something of a middle ground. The police were neutral, but they were not hostile, while the university president’s authority gave them full cooperation with the university staff, which was probably more valuable to them. In future mysteries, it’s likely to be different based on who is asking for help.