The OSHC was a Starfleet agency that investigated the disappearance of Marla E. Finn from Utopia Planitia Fleet Yards in 2362. The investigation ended inconclusively on stardate 40999.4. This fact was noted in Finn's personnel file. (TNG: "Eye of the Beholder")
The abbreviation may stand for Operational Safety and Health Command, which would mirror the modern US OSHA agency.