Green’s Dictionary of Slang

1. (US Und.) a women’s prison.

1931–4		D. Clemmer Prison Community (1940) 332/1: finishing school, n. A reformatory for young girls.
1949		Monteleone Criminal Sl. (rev. edn).

2. (US Und.) reform school for boys.

1956

‘Vin Packer’ Young and Violent 48: He got sent off to finishing school. Came up this morning in lolly-pop court.