Lipman, Crockett and Higgins have played over 100 games each for Bath
Bath's joint captains Michael Lipman and Alex Crockett and winger Andrew Higgins have resigned from the club.
Their decision came immediately before they were to appear at an internal hearing into an alleged failure to take drug tests on three occasions.
But the players said "scurrilous and unsubstantiated allegations" had forced their exit and that they had not refused anti-doping drugs tests.
The Rugby Football Union says it is looking into the matter.
England international flanker Lipman, 29, joined Bath from Bristol in 2003 along with Higgins, 27, while centre Crockett, 27, came through the ranks.
The trio issued a joint statement through their solicitor Richard Mallett, and said they had been forced out of the club.
It has been suggested in sections of the media that we have refused to provide samples for anti-doping purposes, but this is untrue
Statement issued on behalf of Lipman, Crockett and Higgins
"It is with tremendous regret that we announce that, as a result of the club's actions, we have no option but to terminate our contracts with Bath Rugby with immediate effect," read the statement.
"During the course of the last few weeks it has become clear to us that our position within the club has been made untenable.
"We have made every effort to work with the club to resolve our differences. Sadly, we have been unable to do so.
"It has been suggested in sections of the media that we have refused to provide samples for anti-doping purposes, but this is untrue.
"Anonymous sources have also made allegations against us to the club. We completely refute these allegations, which are both false and defamatory.
"We believe that these scurrilous and unsubstantiated allegations are not only proving to be damaging to our own careers but to rugby as a whole.
"We have all been immensely proud to have represented Bath Rugby and we are extremely grateful for all the support which we have enjoyed from the players and the club's amazing and loyal fans.
"Whilst we are extremely disappointed to have to leave the club in these circumstances we wish the players and the fans every success in the future."
The club regards this as an internal matter and intends to make no further comment
Bath chief executive Bob Calleja
Bath chief executive Bob Calleja launched an investigation when a number of the squad were involved in a fracas with players from Premiership rivals Harlequins in London on Sunday, 10 May, the day after their Guinness Premiership semi-final defeat by Leicester.
Calleja said in a statement on the club's website: "Michael Lipman, Alex Crockett and Andrew Higgins had been required to appear at an internal disciplinary hearing today to address the failure on three occasions to take a drugs test following allegations surrounding player conduct on Sunday, 10 May.
"Immediately before the hearings were due to take place the players resigned from the club with immediate effect. The club regards this as an internal matter and intends to make no further comment."
The Rugby Football Union has asked Bath for details of their internal investigation and could take action against the players.
A statement read: "The RFU Disciplinary Officer will review all the information before deciding if there is a broader charge for these players to answer."
Lipman's last England cap came against New Zealand last November
Lipman has 10 England caps to his name and has played 127 games for Bath.
The Professional Rugby Players Association said it was touch with the players and their legal representatives as well as Bath.
"The PRA is extremely concerned about the very serious allegations made publically against three Bath players, and the conflicting statements made by the club and the players regarding their recent conduct," said the PRA in a statement released on Tuesday.
Crockett, who has played for England Saxons, represented the club in 125 games scoring 21 tries, while Higgins scored 28 times in 111 appearances for Bath.
The trio follow Justin Harrison in leaving, the 35-year-old having left by mutual consent last month.
Having signed prop David Wilson, number eight Ben Skirving and former player Olly Barkley, coach Steve Meehan had suggested he was set to bring in just one more player before the new campaign.
But with Lipman, Crockett and Higgins following Harrison out of the club and South African fly-half Butch James sidelined by a knee ligament injury, Meehan now has significant rebuilding to do ahead of the new campaign.
Bath were rocked by the positive drugs test and two-year ban England prop Matt Stevens received earlier in the season.