It appears Sorawee's solution works perfectly. The contract is for a class method; hence, the entry for this. I'm very impressed with Racket's contract system!
[ get-user-data
(->i ([ _ any/c ] ; this
[ conn connection? ]
[ reference-key string? ]
[ type string? ])
(values [ hsh (or/c hash? #f) ]
[ errors (hsh) (if (hash? hsh)
'()
(listof string?)) ])) ]
P.S. It looks like someone may have marked the previous reply solved prematurely, maybe an admin/moderator? May I humbly suggest we wait a period of time to allow the OP to mark a solution before doing so on their behalf? I was busy yesterday evening, so I was only able to test the solution today.