The superintendent of Southbridge public schools resigned on Friday, a little more than two months after being placed on paid administrative leave over an allegation of misconduct, the chairwoman of the School Committee said Sunday. Eric D. Ely was hired to lead the district in 2010, said School Committee chairwoman Patricia Woodruff, and resigned in a phone call without giving a reason. Ely had been placed on paid leave on Nov. 14 after an allegation was made against him, said Woodruff, who declined to explain the allegation beyond classifying it as a personnel matter. It was not financial, she said, and police were not involved. The district hired an acting superintendent in December, she said, and he will be voted in as the interim superintendent in February. The district is hoping to find a new full-time superintendent by the end of June. Ely’s annual salary was about $135,000, said Woodruff.