Simply playing a song "in the background" without any critique, educational purpose, or other transformative fair use is almost certainly an performance of the original work. If the cop doesn't have an appropriate license, they could be liable for statutory damages up to $150,000[1] per work.

Unfortunately, enforcing this will probably only happen if someone with standing files a lawsuit. I doubt many music labels that hold the relevant copyrights are interested in suing the cops.

[1] damages normally start much lower, but the performance of the copyright protected work is patently willful