Del. Code tit. 9, § 331

Should any 2 or more persons voted for as officials of the county governing body receive an equal and the highest number of votes cast at any election, the Superior Court, sitting as a board of canvass in the county in which the tie vote occurs, shall certify the fact to the Governor who shall forthwith appoint 1 of the candidates involved in the tie to be 1 of the county governing officials for the county. The person appointed shall hold the office for the term of 2 years from the first Tuesday in January then next ensuing.