The noun "police" refers to a group of persons in English, or even (more abstractly) to all police officers. To say that you as an individual are not one, you would need to say "I am not a policewoman," "I am not a policeman," "I am not a police officer," or (colloquially) "I am not a cop."
If you were wondering if the Turkish could also mean "I am not a police officer" (etc.), I was wondering that too. I think that "Ben polis değilim" can mean that, but I'd like to be sure!
"yok" is the opposite of "var" and is used to deny the existence of something. If often equates to the English "There is not..."
"değil" is used to negate sentences without a verb that don't have to with existence. It often equates to the English "am/is/are not"
This has a somewhat different meaning in English. You often hear this ("I am no [X]") followed immediately by ", but ..." E.g., "I am no policeman, but that guy should have been arrested." A better translation here would just use "not" for "değilim": "I am not the police officer" or (I think) "I am not a police officer."
Also, "I am not the police officer" would need to occur in a broader context to make sense in English. Hearing only this sentence, a listener would ask, "Which police officer do you mean?" You're much more likely to hear "I am not the police officer you saw at the park," or some such additional language that provides more context.