The best answers I found on Google were ones like this which is basically "because lots of Irish people were in the police in the 1800s because of discrimination" but doesn't actually explain much:
If anyone knows the history of the bagpipes in American police forces, I'd love to learn it in more detail! Thanks!
Part of the problem is that the Irish counterpart to the Great Highland Bagpipe, which is the Irish War Pipe (featuring two as opposed to three drones), was not produced on a scale or a consistency to allow early North American pipe bands (or even solitary pipers!) to obtain Irish pipes as was easily as the Scottish variety. At the same time, the uilleann pipes have tended to be more popular in Ireland - and among immigrant Irish - than the Irish War Pipes. Because the quieter, non-military uilleann pipes would not be suitable for an outdoor ceremony - particularly when something marshal was called for - it was natural to default to a mouth-blown, louder part of the bagpipe family, and given that, the Great Highland Pipes were really the only realistic option. Some Irish pipe bands have recently adopted the Irish War Pipes, but that has been a recent development that reflects late-twentieth-century mass production of the Irish War Pipes.
I'm not prepared to discuss the other question about how pipes became associated with police and other funerals, even without an Irish or Scottish presence. I can tell you that my Pipe Band, the Sierra Highlanders Pipe Band was organized in 1961. It was initially conceived as a police pipe band, but lacking sufficient numbers, membership was opened to the larger community. Membership in the band has consisted of every type of Celt one can imagine, and a fair share of other people representing a wide swath of ancestry. The band has consistently played for police funerals since it was organized.
There are a few points you may find interesting in the last tread I recall on bagpipes, which links to one in particular that talks about the association between bagpipes and the military