The Commissioner shall, when submitting the estimate of revenues and expenditures for the Department of Social Services, include therein a statement of the rates fixed by the state to be paid by the County to hospitals, institutions for the aged, institutions for children, nursing homes, correctional institutions and foster homes and other institutions and a recommendation as to any rates not fixed by the state to be paid by the County for services rendered for the care and maintenance of persons for whom the Department of Social Services is responsible. Such rates, once approved by the County Executive, shall be included in the tentative budget. The County Legislature shall, by resolution and as part of the budget procedure, approve the rates fixed by the state and determine, fix and establish the rates to be paid by the County for services where the rates are not fixed by the state.