Isn't that public performance and doesn't that require the police dept to pay royalties?
Yes, but under current law, states can ignore the royalty requirement with impunity: "[C]opyright owners suffering infringement by state entities cannot seek the remedies provided by the Copyright Act." [0]
Police departments are almost certain to be held to be state entities, I'd think, and therefore immune from individual personal liability for copyright infringement liability.
And the doctrine of "qualified immunity" might shield the police officer from personal liability for infringement as well.
But I haven't looked into this specific issue.
(Usual disclaimer: I'm an IP lawyer but not your lawyer.)
[0] https://www.copyright.gov/policy/state-sovereign-immunity/