“The state already has the buildings,” said Laura Butler, a state social worker. “It just needs to hire the staff, and the problem is solved.”

Many people who face criminal charges are ordered by judges to undergo psychological evaluations or treatment if they are too mentally ill to understand their surroundings or comprehend that they have committed a crime.

A Washington Post analysis this year found that Maryland’s state psychiatric hospitals had 1,000 beds in 2012, with most of them filled by people transferred from jails.

Consultants for the state estimated in 2012 that the hospitals needed more than 200 additional beds, but the health secretary at the time rejected that conclusion, saying the state could relieve the pressure with better management and increased use of community-based treatment.

Judges have complained that the state is defying their orders and effectively allowing people to be detained illegally. Some have required health officials to appear in court to explain why they should not be held in contempt.

Maryland Health and Mental Hygiene Secretary Van Mitchell has asked the courts to be patient, noting that he recently spent an extra $8.2 million on staffing and overtime to help address the situation. He also created a work group to develop solutions.

The task force completed draft recommendations in July, calling for the state to increase bed capacity at its residential treatment centers and expand outpatient services for people who are required by court order to seek help.

Mitchell also has said that he is exploring options for placing some patients in private hospitals, and that he wants to request construction of a state-of-the-art mental-health facility that would be the first new state-run hospital in more than 40 years.

“The timing of the union’s rally is significant and underscores what the state of Maryland already has been saying and doing this year about this issue,” health department spokesman Christopher Garrett said Monday. “The department has been demonstrably engaged on what has been a years-long problem.”

Advocates said the department’s efforts to hire more staff might come in vain unless it also addresses what they described as inadequate pay for state mental-health workers relative to the salaries they can earn with private organizations.

“I personally have $251,000 in student loans, and that covers only my post-college education costs,” said Heather Adams, a state-employed psychologist. “I have colleagues who worry every day how to pay for a place to live, food to eat and child care. Individuals with higher education cannot afford to work in state hospitals due to non-competitive wages and high-cost student-loan repayments.”