Brewer's Dictionary of Phrase and Fable suggests the police wagon was named after a fearsome lady called Maria Lee who kept a boardinghouse in Boston in the 1820s.
It was said the police would call her in to help with unruly prisoners.
Which sounds unlikely when they could simply whack them with a big stick.
The World Wide Words site on the internet says the first reference to a Black Maria vehicle in Boston was in 1847, some years after the lady's fame.
A likelier connection could be a famous race horse named Black Maria whose greatest victory was a 20 mile race run in New York in 1832.
Three years later, police vehicles in the city became known as Black Marias.