How can you prove harassment by the police department? At what point is it considered harassment?

You can prove harassment in several ways, whether the alleged perpetrators are members of a police department, specifically, or anyone in general. Firstly, you must assess what type of harassment you are experiencing. Is it physical, verbal, or electronic harassment? Or is it a case of stalking? If the latter, the police department has the legal right to conduct physical and remote surveillance, for as long as they have a legitimate reason to do so, such as an active criminal investigation in which you are a suspect.
If you believe you were verbally abused by a police officer (i.e., you were called a racial slur or other derogatory terms), find out if there were any witnesses to this event and if it was recorded. You must then track witnesses through legal means or find digital copies of any audio or video recordings of the event.
Most importantly, you must study state and federal laws and learn the legal definitions of what is considered harassment. If the supposed harassment that you experienced from members of the police department fit within these legal definitions, you can contact an experienced attorney to look over your case. You can also contact the police department's internal affairs division and file a formal complaint.