Section 11A. When a public way other than a state highway has been constructed or improved in whole or in part by aid of money contributed by a county, the said way shall be kept and maintained in good repair and condition by the town in which the same lies, but the county may aid in such maintenance, and for such purpose the county commissioners may grant sums of money from the county treasury to be paid to the town to aid in such repairs as the commissioners may order. Such money may be paid to the town from time to time as the work progresses to the extent that the commissioners are satisfied that the same is being done in accordance with their directions. Such grants or contributions shall not render a county liable for defects in any way or for damages to persons traveling thereon, and when the work of repair or maintenance for which such grants or contributions are made is completed there shall be no further obligation on the part of the county as to the repair or maintenance thereof until a further grant or order is made by the county commissioners for such purposes.