You capitalize 'police' after the department name, where the word is part of the department name, as in, 'The Somerville Police Department is looking to recruit more policeofficers.'
No, not unless the word 'police' was part of the official name being used (for instance: United State Park Police - New York City Police Department.)
no
Yes, you do capitalize the word department when it directly follows the name of that department. This is the case when signing letters or referring to specific departments in emails or in writing.
Yes.
NYPD (New York police department
No, "police" isn't a proper noun in this case, if I read your question correctly. It would be proper if you wrote New York Police Department or something like that.
The "T" in "treasury" is capitalized when it is part of a proper noun, like in the name of a specific treasury department or office (e.g., U.S. Treasury). Otherwise, in general use, "treasury" is written with a lowercase "t."
No it should only be capitalized if it precedes a name.
Police is a common noun. Proper nouns name a specific police officer or a specific police department. Examples: Officer Glen Martin The Glendale Police Department
Yes, Federal Police should be capitalized when referring to a specific organization or entity, such as the Federal Police in Mexico or the Federal Police in Germany.
Yes.
Internal Security Department
They are officially known as "The Hong Kong Police Force."
Yes, but they do not share the information.