It depended on the colony and its regulations. Here are some examples: New netherlands slave imports began as a part of the state government. Enslaved people were initially only held in bondage by the government itself (starting in 1620) and they were forced to build the city infrastructure and produce staple crops to feed the city. Only later were slaves allowed to be sold to private individuals and laws regulating slavery were passed.

Virginia: Enslaved people were sold by a passing ship carrying a small cargo of slaves to local people. More and more slaves were sold over the years and laws regulating slavery were passed as the population grew.

South Carolina: founded by barbados planters. They brought slaves with them at the outset and imported the barbados slave codes.

Georgia: slavery is initially illegal (the only state to make that so). Slaves are rented from SC or held illegally and wealthy Georgians lobbied for a legal change in the 1750s.

The idea that police officers existed, well....that just wasn't the case. Big cities didn't get police officers until the 1820s. Police duties were something done by other government officials in the course of their duties.