Back when the Irish were considered an 'other' and like vampiric monsters sucking all the jobs out of America, there was a period where they slowly started working as pigs (cops) because nobody else wanted to do that bullshit at first.
So when criminals were loaded up in a carriage, the wagons were called 'paddy wagons' due to cops mostly being Irishmen and back in Britain paddy was a slur for an Irishman.
I do apologize for my fellows for being pigs.
Maybe this is common knowledge? I'm not sure.
It also has a bit to do with timing, by the time Irish people were being given jobs in the police other immigrant groups were starting to become more prominent in a lot of US cities and prejudices slowly moved away from anti-Irish to other groups. You see similar in the UK with Caribbean immigrants becoming a lot more accepted into society by the time large scale immigration from Asia became the next big racist bugbear.