See Full Constitution
Article III

Section 4. Contested elections of Governor or Lieutenant-Governor

Contested elections of the Governor or Lieutenant-Governor shall be determined by a joint committee, consisting of one-third of all the members elected to each House of the General Assembly, to be selected by ballot of the Houses respectively. Every member of the committee shall take an oath or affirmation that in determining the said election he or she will faithfully discharge the trust reposed in him or her; and the committee shall always sit with open doors.
The Chief Justice, or, in case of his or her absence or disability, the Chancellor shall preside at the trial of any contested election of Governor or Lieutenant-Governor, and shall decide questions regarding the admissibility of evidence, and shall, upon request of the committee, pronounce his or her opinion upon other questions of law involved in the trial.