Cop answer

The police-specific use of “cop” made its way into the English language in languid fashion. “Cop” has long existed as a verb meaning “to take or seize,” but it didn’t begin to make the linguistic shifts necessary to turn it into a casual term for “police officer” until the mid-19th century. The first example of “cop” taking the meaning “to arrest” appeared in 1844, and the word then swiftly moved from being solely a verb for “take into police custody” to also encompassing a noun referring to the one doing the detaining. By 1846, policemen were being described as “coppers,” the ‘-er’ ending having been appended to the “arrest” form of the verb, and by 1859 “coppers” were also being called “cops,” the latter word a shortening of the former.
From snopes.com