Dignam asks Billy about Uncle Jackie's funeral:
Billy: I remember his funeral.
Dignam: Closed casket?
Billy: That's right.
Dignam: So tell anybody up at Deerfield... Before you got kicked out for whaling on a gym teacher with a chair. You had an Uncle met his demise like that? I got a question. How fucked up are you?
What did Dignam want Billy to tell at Deerfield?
Looking to the full context of the screenplay:
SGT. DIGNAM (getting to business, hard) You have family connections down in Southie. Through your father. Tell us about your uncle Jackie.
BILLY Uncle Jackie was a carpet layer for Jordan Marsh.
SGT. DIGNAM Uncle Jackie was a small-time bookie who tended bar at the Vets in Somerville. He got popped by Nicastro in '95. They found his body out by the airport.
BILLY That's right. (tightly) I remember his funeral.
SGT. DIGNAM (cruelly) Closed casket?
BILLY That's right.
SGT. DIGNAM You tell anybody at Deerfield - that is, before you got kicked out for whaling on a gym teacher with a folding chair - you had an uncle met his demise like that?
For more explanation, 'Deerfield' is Deerfield Academy, an upscale prep school where Costigan likely tried to get far away from his family to start a life without stigma like that mentioned of his uncle.
Dignam is asking Costigan sarcastically if he told anyone at this school how 'fucked up' his life really is.
