The Department of Health and Human Services yesterday made official the appointment of Dr. Scott Nelson, a mental health administrator for the state of Pennsylvania, as superintendent of St. Elizabeths Hospital.

A Harvard-trained psychiatrist, Nelson has been deputy secretary for mental health of Pennsylvania's Department of Public Welfare since January 1980. He held a similar position in the New Mexico Department of Hospitals and Institutions.

In 1975, Nelson worked as an administrator in the federal Alcohol, Drug Abuse and Mental Health Administration, the agency that monitors St. Elizabeths. Earlier, Nelson served as the medical officer and mental health officer of the Job Corps.

Nelson, 43, assumes his new post at a critical time for the 127-year-old federal hospital, which is struggling to deal with an expected $25 million deficit and a continuing attempt by the federal government to shift financial responsibility for the mental institution to District taxpayers. Large-scale layoffs of staff and patient workers have been ordered by federal officials, as well as cuts in several treatment programs.

A spokeswoman for Nelson said he would have no comment on his appointment.

Nelson's salary as superintendent will be $80,697. Because Nelson is a member of the Public Health Service Commissioned Corps, his pay includes special subsistence pay, monthly quarters allowance, a housing allowance, extra pay for his certification by the American Board of Psychiatry and Neurology, special retention pay and a supplementary allowance because of his medical degree, explained James Helsing, a spokesman for the Public Health Service.

Nelson replaces Dr. William Dobbs, who is stepping down after 29 years at the hospital.