Despite a nationwide contract settlement last week, a telephone strike in the Washington area may begin at midnight tonight if agreement on local issues is not reached. Bargaining is under way between the Chesapeake & Potomac Telephone Co. and representatives of its 31,000 unionized employees.

A spokesman for the Communications Workers of America said yesterday that local contract talks, being held at the Shoreham Hotel, still have "a number of real probles." He said he was hopeful that an agreement could be reached before the strike deadline.

A spokesman for C&P, which provides telephone service in Washington, Maryland, Virginia and West Virginia, said the company also was "pretty optimistic."

The nationwide settlement reached last Saturday covers wages, pensions, health insurance, and other major economic issues affecting the Bell System's 700,000 unionized workers.

However, the company and the union still are trying to reach agreement on 37 local contracts, including the one at C&P.

George Strick, a CWA vice president of the union's Region Two, who is conducting negotiations with C&P said the main issues still awaiting settlement here are new rules covering lay-offs and reassignments, and provisions for arbitrating grievances.

Because of automation, C&P has reduced its unionized work force in the Washington area from 12,500 to 10,100 over the past six years.

So far, all the cutbacks have been achieved by attrition without any telephone workers being fired, but union leaders have called the trend "frightening." Yesterday, Strick said the lay-off provisions of the local union's old contract were "antiquated."

Lee White, a spokesman at the CWA's national office, said none of the 37 local contracts had been settled by late yesterday, but he remarked:

"That's not disturbing because in collective bargaining it is always difficult to get an agreement until just before the deadline."