(a) The governing body of a county, the chief administrative officer in Montgomery County, or the supervisor in Baltimore City for any local taxes that are due, shall make allowances for:

(1) insolvencies or removals as to personal property;

(2) refunds made under law; or

(3) decreasing or abating assessments under § 8-419 of this article.

(b) On certificates by the governing body of a county, the chief administrative officer in Montgomery County, or the supervisor in Baltimore City, the Comptroller, for any State taxes that are due, shall make allowances for:

(1) insolvencies and removals as to personal property;

(2) refunds made under law; or

(3) decreasing or abating of assessments under § 8-419 of this article.