While New Hampshire will provide psychiatric care for its prisoners by contracting directly with Dartmouth’s department of psychiatry, Massachusetts has chosen a different path. There are 10 major prisons and 14 smaller units in the Massachusetts system. Out of 10,000 inmates, about 18 percent have open mental health cases, said Kenneth Appelbaum, M.D., director of correctional mental health programs at the University of Massachusetts Medical School in Worcester. Bridgewater State Hospital contains 300 inpatient beds and is used for forensic evaluation.