NEW YORK (AP) ― Producers of Broadway’s “Spider-Man: Turn Off the Dark’’ have fired back in their legal fight with one-time director Julie Taymor, claiming the woman who they once called a visionary later failed to fulfill her legal obligations, wrote a “disjointed’’ and “hallucinogenic’’ musical, and refused to collaborate on changes when the $75 million show was in trouble.

In a countersuit filed Tuesday in U.S. District Court for the Southern District of New York against Taymor and her company, LOH Inc., the producers argued that the show “is a success despite Taymor, not because of her.’’

The lawsuit, which quotes from several private emails from members of the creative team, further exposes the deep rift that has opened between former collaborators who seemed to have reconciled ― at least through forced smiles ― on the red carpet this summer when the musical finally officially opened.

Taymor, who had been the original “Spider-Man’’ director and co-book writer, was fired from the musical in March after years of delays, accidents and critical backlash. The show, which features music by U2’s Bono and The Edge, opened in November 2010 but spent months in previews before officially opening a few days after the Tony Awards in June.

In November, the Tony Award-winning director slapped the producers ― led by Michael Cohl and Jeremiah J. Harris ― as well as Glen Berger, her former co-book writer, with a copyright infringement lawsuit, alleging they violated her creative rights and haven’t compensated her for the work she put into Broadway’s most expensive musical.

In the new filing, the producers’ counterclaims assert the copyright claims are baseless. They also argue that although Taymor was paid to co-write and collaborate on the musical, she refused “to fulfill her contractual obligations, declaring that she could not and would not do the jobs that she was contracted to do.’’ They claim Taymor repeatedly refused to work on changes with other members of the production team.

The producers claim she “caused numerous delays, drove up costs, and failed to direct a musical about Spider-Man that could open on Broadway.’’ Her version of the superhero story, they assert, bears little resemblance to the show that is currently playing at the Foxwoods Theatre.

“Taymor refused to develop a musical that followed the original, family-friendly ‘Spider-Man’ story, which was depicted in the Marvel comic books and the hugely successful motion picture trilogy based on them. Instead, Taymor, who admits that she was not a fan of the ‘Spider-Man’ story prior to her involvement with the Musical, insisted on developing a dark, disjointed and hallucinogenic musical involving suicide, sex and death,’’ the producers charge in the lawsuit.

They claim Spider-Man was “relegated to a supporting role’’ while a new Taymor-created villain character named Arachne took center stage. In the version that opened after Taymor left, the role of Arachne was substantially cut.