Priority in multiple claims to refunds allowed to be setoff under the provisions of this article shall be determined by the following classifications and in priority order as follows:

1. Claims of the Department;

2. Claims filed by the Department of Social Services, Division of Child Support Enforcement;

3. Claims filed by any court or other administrative unit of state government;

4. Claims filed by any county, city, or town; and

5. Claims filed by the Internal Revenue Service. Priority for claims within the same classification shall be determined by the order in time in which the claimant agency filed a written notice with the Department of its intention to effect collection through setoff under this article. Claims filed by counties, cities and towns for an offset of the federal income tax refund shall be limited to claims for delinquent local taxes.