A tortuous 15-month-old labor dispute in Prince George's County that has included a strike and a confusing array of court proceedings went into yet another round yesterday -- all over the long-delayed signing of a contract that is due to expire two months from now.

Yesterday, a three-judge panel ruled that County Executive Lawrence Hogan is not required to sign the contract, although a Circuit Court judge earlier this week had ordered him to do so.

The tug-of-war over the signing of the contract with the county's 1,500-member public employes union has been going on ever since a tentative agreement was negotiated in February 1980. The case has gone all the way up to the state's highest court, and back down again through the county courts. Now, lawyers for the American Federation of State County and Municipal Employees say they will return to court Monday, again seeking an order to force Hogan's signature.

But whatever happens, the Contract in dispute is one that covers the period between July 1, 1979, and June 30, 1981, when it will expire.

"We're still in court, and it's almost June 30 again," said Herbert Belgrad, one of the union's attorneys. "If only the county would expend its time and effort and funds to live up to the terms which every court has found it must, instead of expending time and effort and funds to obstruct the orders, then perhaps there'd be some labor peace in Prince George's."

But county attorney Robert Ostrom said the county should not have to live up to an agreement that he maintains the union breached by striking last August. "What we should be doing is negotiating for the future and present . . . not the past," Ostrom said yesterday.

The long-running labor dispute began in February 1980 when negotiators for the union signed a tentative agreement considered favorable to the county.

However, when the contract was presented to Hogan for his final approval, he blew up with anger and refused to sign it, according to county officials familiar with the incident. What angered Hogan was not the contract, but statements by political adversaries on the County Council who criticized his handling of the negotiations.

The union took the case before a hearing examiner, who ruled that Hogan had violated county labor laws by vetoing the tentative agreement because of political considerations, and the examiner ordered him to sign it.

Circuit Court Judge Jacob S. Levin upheld that finding last July, and the county appealed. The state's Court of Appeals last January upheld Levin's ruling.

Meanwhile, in August 1980, union members, including clerical and maintenance workers, road repair crews and jail guards, went on strike for 11 days, but returned to work and voted to pursue the matter in court.

On Monday, an obviously angered Judge Levin again ordered the county to comply with the tentative agreement, and the county appealed to a three-judge panel. The panel ruled yesterday that the union had chosen an inappropriate legal route for relief and reversed Levin's order.

Union attorney Belgrad said yesterday the union will return to court Monday to seek the proper remedy to get the contract signed. But Ostrom is already arguing that it is too late for the union to take a new course of action.

Meanwhile, the union workers are continuing to receive the pay and fringe benefits prescribed in the February 1980 agreement. But, according to Belgrad, members are working without grievance procedures and other contract benefits as long as Hogan refuses to sign.