Can the police charge me with a crime?

No.

 

The police can only investigate and arrest.

 

When they arrest you, the police will identify a criminal charge, but that is not and may not be the actual charge filed.

 

The prosecutor, not the police actually begin the process of bringing you before a judge and jury.

 

The actual charging document is called a ‘Prosecutor’s Information’ or an ‘Indictment’.