Yes, CUSTODY is a Scrabble word!

Letter values in Scrabble US: C 3, U 1, S 1, T 1, O 1, D 2, Y 4.

Is it a valid word?

CUSTODY is a valid word in the official Scrabble dictionary (US), the UK Scrabble Dictionary and Words with Friends (ENABLE).

a state of being confined (usually for a short time)
holding by the police
(with `in') guardianship over; in divorce cases it is the right to house and care for and discipline a child