The Departments of Correction, Children and Families and Mental Health and Addiction Services, and the Court Support Services Division of the Judicial Branch may include in the estimates of expenditure requirements transmitted pursuant to § 4-77, and the Governor may include in the Governor’s recommended appropriations in the budget document transmitted to the General Assembly pursuant to § 4-71, an estimate of the amount required by said agencies for expenditures related to the implementation of evidence-based programs.