Prince George's County Executive Lawrence J. Hogan, who resisted for 15 months signing a bitterly disputed contract with the county's public employes union, finally signed it last night, but only after a judge ordered him to do so.

He then sent it to the County Council along with a five-page letter urging the council to refect it.

That plea from the Republican executive apparently fell on unsympathetic ears. Several members of the all-Democratic council said they expect to sign the contract that Hogan had refused to honor since negotiators for the county and the union reached tentative agreement on it in February 1980.

Hogan's refusal to sign the document led to a 11-day strike in August 1980 by county employes including clerical and maintenance workers, road repair crews and jail guards who were members of the county's locals of the American Federation of State, County and Municipal Employes. Lawyers for the union took their case against Hogan's refusal through the state court system, arguing successfully that the executive was guilty of unfair labor practices.

Finally, last week, Hogan exhausted his court appeals and was ordered to sign the contract by Circuit Court Judge Robert Mason. The contract is retroactive to July 1979 but expires in two months.

In his letter to the council, Hogan made a point of denying reports that he refused to sign the contract because he was angered by statements by his adversaries on the council who criticized his handling of the negotiations.

Instead, he said he objected because the contract would force employes to become union members or pay union dues if they stayed out of the union, require taxpayers to pay the salary of a union organizer "who would do no work for the county" and give union leaders 126 days of county-paid time to attend meetings and conventions.

"These two latter items should be expenses of AFSCME," Hogan wrote, "not of the Prince George's County taxpayers."

The pay raises and fringe benefit improvements called for in the contract were long ago granted the 1,500 union members by agreement between Hogan and the council.

In the letter, Hogan railed against the decisions of judges who handled the case, saying the Circuit Court "misinterpreted its function and failed to pass on crucial questions of Maryland Constitutional and municipal law." Hogan also criticized the Court of Appeals, the state's highest court, which he said rules only on a legal technicality "without in any way looking beyond the bare jurisdictional question."

But such concerns apparently are not shared by the council. "The council is ready, willing and able to sign the contract," said council member David Hartlove. "I don't think there's any doubt about signing it."