The 20-day deadlock between the American Telephone & Telegraph Co. and its largest union continued yesterday because three AT&T subsidiaries--including the Chesapeake & Potomac Telephone Co.--could not reach settlement with the Communications Workers of America.

Nationally, 31 of CWA's local units have reached tentative agreement with AT&T subsidiaries, with the only unresolved talks at C&P, Bell Telephone of Pennsylvania and Western Electric's telephone-installation division.

Glenn E. Watts, president of the 525,000-member CWA, said that "serious problems" remaining at the three locals would hold up the nationwide agreement because of CWA policy that none of the 34 agreements will be signed until all are settled.

Last night C&P, which employs 34,000 CWA members in Maryland, Virginia, West Virginia and the District of Columbia, held "active informal discussions" with CWA, but no formal bargaining was scheduled, according to a company spokesman.

Wages, benefits, and other major issues have been resolved in national contract talks, but C&P and the CWA are at an impasse because of company proposals to reassign workers and change job descriptions and pay grades.

Watts blamed the stalemate on what he called AT&T's "take-back demands," which he said were last-minute efforts by local subsidiaries to undermine past contract gains.

An AT&T spokesman said the companies "have been bargaining responsibly since May 19."

CWA's national executive committee also met last night to review progress in the strike, which has idled most of AT&T's 675,000 unionized workers since Aug. 7.