Cops, when referred to police, is an abbreviation for 'coppers' which is slang that was introduced from the USA in the mid 1800s. Sorry, but I don't know why the Yanks called their police 'coppers'.
Note also that the slang word 'cop' also has other meanings; as in 'cop for it', 'cop off', etc.
'Cop' is an old English word meaning 'to catch'. It comes from French 'caper' and, even further back, from Latin 'capere'. That's what a policeman's job is...to catch baddies. Hence the name.
Lots of people say it comes from the copper buttons they are supposed to have had on their uniforms long ago and others say it is an acronym for 'Constable on Patrol'. However, I'd advise you to go with the etymology offered by the word-bible...The Oxford English Dictionary. It says cop = catch is the explanation.
Actually, TW, Jjf isn't correct...unless, that is, The Oxford English Dictionary is wrong. I myself mentioned the copper buttons theory in my answer a day earlier, but that would appear to be no more than an urban legend. The only things coppery the OED mentions in this connection are 'coppersticks' which were a form of early police baton. Cops/coppers are catchers...it's that simple.