The bizarre legal tug-of-war between Chuck Fairbanks, who wants out of his contract as coach and general manager of the New England Patriots, and the team that wants to hold him to the pact that has another four years to run, continued yesterday with no resolution of the puzzling questions involved:

Can the Patriots force Fairbanks to live up to his contract with the National Football League's American Conference East champions, even though he has requested his release so he can coach at the University of Colorado, a job he already has accepted verbally?

Will Colorado follow through and sign Fairbanks to a contract if he is unable to work out his legal problems with the Patriots?

Who will coach the Patriots between now and the end of the NFL playoffs, as the young and powerful team Fairbanks built seeks its first Super Bowl title?

Fairbanks, who came to New England from the University of Oklahoma in 1973 with a contract envied by many NFL coaches, was suspended without pay by Patriot President William Sullivan Monday after he surprisingly asked for release from his obligations so that he could return to college coaching. The Colorado job reportedly offers coaching. The Colorado job reportedly offers $45,000, but is sweetened by lucrative side deals that would net Fairbanks well in excess of his current salary, estimated at $150,000 per year.

Fairbanks asked to remain with the Patriots through this season's playoffs, but was told by Sullivan that it "is impossible to serve two masters." Sullivan suspended the coach immediately and, in an acrimonious scene before the Patriots' 23-3 loss to the Miami Dolphins Monday night, ordered Fairbanks out of the team's locker room.

Sullivan said it would be impossible to have Fairbanks as a lame duck coach during the playoffs, but apparently had an abrupt change in attitude yesterday. Chuck Sullivan, the owner's son and an attorney who serves as vice president and counsel of the Patriots, said from his New York office that the team is willing to have Fairbanks coach through the playoffs and will negotiate with him after the season ends.

"We're not going to release him, not at all," the younger Sullivan said last night. "But right now, we'd just like to concentrate on making the Super Bowl."

The Patriots called a press conference for late yesterday afternoon, presumably to name a head coach, then canceled it, prompting speculation in Boston that Fairbanks would be allowed to coach the team the rest of this season and then would be released from his contract.

WBZ also reported that Chuck Sullivan had been in communication with high adminstration officials of the University of Colorado, and had received assurances that the school would not sign Fairbanks until his contract difficulties with the Patriots were resolved.

Colorado Athletic Director Eddie Crowder said at a press conference in Denver, however, that Fairbanks will coach there next season, and already has hired two assistants: Jerry Pettibone and Gene Hochevar.

"He wants to coach here, we want him here, and he will coach here in 1979," Crowder said. "I haven't heard the reports out of New England. All I know is that I talked with Chuck this morning, and he said he'd take the job. We've been close friends for 20 years. Neither of us felt there was any need to formalize our agreement in writing."

But, Crowder conceded, "He technically was not offered the job until he had a chance to sit down and talk with the owners of the patriots. It was a subtlety that he would not have a job here until he settled things with New England."

Crowder said Fairbanks wanted to resettle his family in the west and resume college coaching, and that his decision had "little to do with compensation."

He said Fairbanks woudl be paid $45,000 annually, plus an undetermined amount for television and radio shows, but "very likely will be making less here thant at New England."

Crowder emphatically denied reports that Fairbanks had been promised substantial income from a Denver golf resort development planned by oilman Jack Vickers, and Vickers- a longtime friend of Fairbanks- called these reports "hogwash."

Crowder revealed that he had offered the Colordao job to St. Louis Cardinal Coach Bud Wilkinson, who has coached Crowder at Oklahoma. "But he said he had commitments at St. Louis which he felt he should see through," Crowder added.