Over the years I've seen the word used in various ways:

A "cop" on a beat.
"Cop a feel" on a date with your girlfriend.
"Cop a squat" to sit down often on the ground.
"Cop a plea" attempt to be charged with a lesser crime.
"Cop to it" to admit to something.

I don't actually recall using the word in any sense other than the first.

k