State auditors wrote Gov. Dannel P. Malloy on Monday to tell him they discovered that the state overbilled $3.4 million in Medicaid claims to the federal government.

The auditors initially reviewed 25 claims totaling $257,280 and found one for $1,920 for a patient who had already been discharged from the Department of Children and Families’ Albert J. Solnit Psychiatric Center in East Windsor. An additional 17 monthly claims totaling $145,920 were filed on behalf of another patient, also already discharged.

So the state auditors decided to dig a little deeper and tested 20 more claims involving eight patients totaling $1,086,980. The auditors found dates of service that fell outside the patient’s admission and discharge dates in that group of claims.

The Department of Administrative Services, which acts as the billing agent for the state, got involved as well and concurred with the findings of the auditors.

DAS identified an additional 55 monthly claims totaling $2.19 million that required adjustments. Some of those claims were outside the fiscal year that ended June 30, 2012. During the investigation, DAS discovered the state continued to bill the federal government for at least one patient who was discharged from the facility in 2005. The billing for the services continued from January 2006 through January 2009 for that patient.

Since the state receives at least 50 percent reimbursement for the Medicaid claims, the federal government now has a credit of about $1.7 million against future Medicaid claims, DAS spokesman Jeffrey Beckham said Monday.

The computer system continued to bill the federal government until a discharge date was manually entered into the system.

“We have put in place a new review system to ensure this doesn’t happen in the future,” Beckham said.

State Auditors John Geragosian and Robert Ward discovered the problem during the course of their regular audit schedule.

DCF’s Albert J. Solnit Psychiatric Center, which was previously known as the Children’s Center, provides services to Medicaid-eligible children and adolescents consisting of comprehensive care to youth with severe mental illness and related behavioral and emotional problems.

It’s the second time in recent weeks that the Department of Children and Families has been cited for overbilling the federal government.

On Dec. 17, the Office of Inspector General found that the agency billed about $1.3 million more than it should have for training its employees. Of the $6.38 million that the state claimed for Title IV-E training costs, only $5.1 million complied with federal requirements.