Unclaimed personal property of deceased patients and of other former patients of any charitable hospital which is supported in whole or in part by county funds shall be held at each institution, awaiting claim therefor, for a period of one year, after which time under the direction of the county treasurer of the county maintaining such institution, and at a time to be named by him, the property may be sold at public or private sale. The proceeds of the sale shall be turned over to the treasury of the county.