The Department of Health and Human Services and the Department of Correctional Services shall have authority to petition the authorities of any city, town, or village in which a state institution is located, to grade, curb, and pave any street or streets upon which the grounds of the institution abut, where the streets are a part of a paving district, to waive any damage sustained by the grounds from the grading, curbing, or paving, and to charge the grounds with a proportionate share of the cost of paving. The contract for grading, curbing, and paving shall be let by the authorities of the city, town, or village, as provided for by the law governing the city, town, or village, and none of the provisions for the letting of contracts by the department shall apply. The cost of paving, including curbing and grading, assessed and levied against the property, shall be paid to the proper officers of the city, town, or village, by the State Treasurer, out of funds which may be appropriated by the Legislature for that purpose.