Public domain? Although state and local police are not prohibited from claiming copyright in their photos the answer depends on the state where the police department is located. Some states like New York, Illinois, and Michigan (called "closed copyright" states) actively pursue copyright for employee-created works. Other states like Virginia, California, and Massachusetts (called "open copyright" states) have a policy that makes state documents presumptively public domain. The Harvard Library has put together a map indicating each state's policy. It's also possible that the police department has created its own policy and granted blanket permission for informational purposes, or that licensing only requires attribution. BTW, photos by federal law enforcement are public domain.
Fair Use? Publication of the photo in your book may qualify as fair use if it provides commentary, expresses ideas “beyond what [the [photographer] expressed in his photographs," or disputes or makes fun of the imagery. When ruling on fair use, courts consider four factors. But, beware, if you claim fair use, you'll likely have to prove your claim in court, an expensive proposition.
What to do? If it's unlikely that the police department will see your book (for example, the photo isn't on the cover) and you're utilizing eBooks and print-on-demand services, you can test the waters by using the image without permission. That way, if a challenge develops, it will be easier to remove the photo without losing a print run. If you're hoping your book becomes popular, or that you sign with a publisher, or you live in a closed copyright state, then, it's best to get permission from the police department.
P.S. Dept. You can find a thorough review of crime photography and copyright issues here.