What’s a precinct constable? You don’t have cops?
Each precinct has an elected constable. That constable has deputies. They have the same power as deputy sheriffs. Texas is full of them. But we especially need them in areas that are heavily populated but not within a city’s jurisdiction. So, no, we don’t have city cops where I live.
http://en.wikipedia.org/wiki/Texas_Constable
http://voices.yahoo.com/what-constable-texas-5445871.html