What were police/investigative services like in America in the late 1700s?

by AokoYume

A friend is writing a short story and needs some information. Her request copy/pasted from a text:

Help! I'm writing a murder mystery short story that takes place in and around 1789, and I'm including letters from an investigator to his superior about the case. Anybody who knows anything about that time period, what was the police/investigation structure, what would his title be, and what position would his superior hold??

Any other information is also welcomed. Thank you!

Georgy_K_Zhukov

More to be said here, but in one of the 'classic' answers of the subreddit, /u/lordkettering dealt with this topic in late-Colonial America. Do check it out!