"Instead, they are distributing a trailer that deliberately confuses consumers into mistakenly believing that Sesame is associated with, has allowed, or has even endorsed or produced the movie and tarnishes Sesame's brand".
The comedy, set to be released in August, is a murder mystery revolving around puppets who exhibit raunchy behavior.
Melissa McCarthy pictured with Miss Piggy and Kermit the Frog in September past year.
Court documents call the trailer "explicit, profane, drug-using, misogynistic, violent, copulating and even ejaculating puppets".
The trailer is showing in select cinemas and is available online for those over the age of 18. To be fair, The Happytime Murders is certainly the polar opposite of what Sesame Street is all about, from the cursing to drug use to the lead puppet character getting, shall we say, overexcited in his office while "servicing" a client.
STX Productions LLC, in a statement issued in the name of "Fred, Esq", a lawyer puppet, said it was looking forward to introducing its "adorably unapologetic characters" to adult moviegoers this summer.
Sesame claims the producers have "diluted and defiled Sesame's beloved Sesame Street children's television show".
Sesame Street has brought joy to young children for decades, and can teach them all kinds of valuable lessons, from letters and numbers to how to be nice to others.
The film is directed by Brian Henson, a direct descendant of The Jim Henson Company who helped develop puppets on Sesame Street when it launched in 1969.
Sesame Workshop alleges in the lawsuit, filed on Thursday in NY state court, that STX Productions has created confusion among the public into believing the film is connected to the show and infringed on the "Sesame Street" trademark.
The lawsuit seems predicated around the fact that the film uses the tagline "No Sesame".
In the film, McCarthy plays a human detective who teams with a puppet partner to investigate grisly puppet murders.
"Sesame has demanded that Defendants simply drop the references to Sesame Street from "The Happytime Murders" marketing materials - a relatively small burden compared to the devastating and irreparable injury Defendants are causing", reads a complaint filed yesterday by Sesame Workshop. They are also seeking unspecified damages.