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.
The police are here. ← This is okay.
*A police is here. ← This is not.
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:
A police officer is here. ← This is okay.
Several officers arrived. ← This is also okay.
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 Police Department is hiring.
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.