Ann Stockett, a 39-year-old Anne Arundel County councilwoman long active in promoting education for the handicapped and mentally ill, was selected by Democratic gobernational candidate Theodore G. Venetoulis yesterday to be his lieutenant governor running mate, according to informed sources.

Stockett aparently is the first woman to run on a gubernatorial ticket in Maryland. Venetoulis, Baltimore County executive and a leading Democratic candidate for governor, has sought a woman to fill the second spot on his ticket since he announced his candidacy.

Elected in 1974 in her first try at public office, Stockett was the state lobbist for the League of Women Voters from 1971 through 1974. She was born in Hagerstown, educated at Hood College in Frederick County and comes from a political family - her cousin John P. Cordeman was a state senator until he was appointed last year to a judgeship.

Venetoulis apparently sent emissaries to a number of camps before making his selection late yesterday. In a primary with at least three major contenders, the lieutenant governor candidate is considered important to the success of each ticket.

Venetoulis choice geographically and politically places his ticket farther from the combination of Acting Governor Blair Lee III and his lieutenant governor running mate, State Senate President Steny H. Hoyer of Prince George's County.

Venetoulis, running as a populist, is trying to portray Lee and Hoyer, both of whom are from Washington's suburbs, as members of the ruling political club.

Hoyer, in fact, was approached by Venetoulis group camp but he decided to run with Lee in the Sept. 12 primary. The Venetoulis group also made initial inquiries to Del. Lucille B. Maurer (D. Montgomery). State Sen. J. Joseph Curran Jr. (D.Baltimore) and former state transportation secretary Harry Hughes, a gubernatorial candidate himself.

Sources close to the Venetoulis camp said Stockett, a mother of two daughters and wife of an administrator of the state's mass transit administration, was selected because her political views closely match those of Venetoulis.

Stockett has sat on or chaired a number of boards concerned with public education, the mentally ill and the handicapped. Among them are: The Anne Arundel County Mental Health Advisory Board, the Barnes Commission on the funding of education and the board of managers of the Anne Arundel General Hospital.

She also is a member of the Stanton Center Commission, an off-shoot of the antipoverty programs, and a member of the board of directors of the Maryland Association of Counties.

A relative newcomer to politics, Stockett had planned to run for a state senate seat this election year and had already printed up a campaign button that read simply "Ann Who"

Venetoulis strategists have said throughout their short campaign battle that a woman, even an unknown woman, would be an important addition to this ticket to underline his assertion that he is proposing a "New Maryland," one open to people outsid the old guard.