In instructional videos I see on the internet, the teacher says "in the U.S and Canada, they automatically use police as plural noun", if it is already plural, then what's the singular of police?
Police is a plurale tantum, a word with no singular form.
Most of the time, if you'd like to talk about a single officer of the law, you say a police officer, or just an officer:
The latter sentence is fine if it's clear from context that you mean a police officer.
But in any case, you can't say *a police.
In this answer, the * symbol indicates that a phrase or sentence is ungrammatical.
When speaking of a particular police deparment/agency/service as a group, the singular form for the group will be something like "Police Department".
The police are coming through the door!
The actual term for a given police department is determined by the official name. For example, the Dallas Police Department or the University of Maryland Police Force.
Snailplane's answer is fine. But since you are asking about the singular term for the word police, it's...
So, as your title asks...