What do puppets do when they are not bringing joy to children?

According to “The Happytime Murders,” a movie starring Melissa McCarthy in which puppets and humans inhabit the same world, the lovable characters get involved in sex, drugs and even murder.

It is not the movie’s raunchy depiction of puppets prostituting themselves, cursing or blowing their heads off that caused Sesame Workshop, the educational nonprofit that produces “Sesame Street,” to file a lawsuit against the film’s creators, STX Entertainment.

It is the use of the tagline “No Sesame. All Street.” in its promotions that tarnishes a brand beloved by millions of children for nearly 50 years, the lawsuit claims.

“We take no issue with the creative freedom of the filmmakers and their right to make and promote this movie, rather this is about how our name is being misused to market a film with which we have no association,” Sesame Workshop said in a statement.

The movie is directed by Brian Henson, a son of Jim Henson, who helped develop “Sesame Street” characters before creating “The Muppet Show.” (Jim Henson died in 1990 at 53.)

Ms. McCarthy plays a police officer teamed with a new partner, who is a puppet, to solve “the brutal murders of the former cast of a beloved classic puppet television show.”

The movie, scheduled to be released on Aug. 17, is described by filmmakers as a “filthy comedy set in the underbelly of Los Angeles.” Brian Henson, the trailer says, is “finally ready to reveal what goes down when kids aren’t around.”

Adam Fogelson, chairman of STX Films, made the same point in April at CinemaCon.

“You know in your hearts, when Kermit the Frog and Miss Piggy go home at night and there are no cameras around and no children, it’s filthy,” Mr. Fogelson said, according to USA Today.

STX released a statement from one of the movie’s characters, Fred Esq., a lawyer.

“While we’re disappointed that ‘Sesame Street’ does not share in the fun, we are confident in our legal position. We look forward to introducing adult moviegoers to our adorably unapologetic characters this summer,” the statement said.

The lawsuit was filed on Thursday in the United States District Court for the Southern District of New York. It maintained that the trailer, which features “profane, drug-using, misogynistic, violent, copulating, and even ejaculating puppets” in combination with the “No Sesame. All Street.” tagline, “tarnishes” the Sesame Workshop brand, whose goal is helping “kids everywhere grow smarter, stronger and kinder.”

For instance, the trailer shows Ms. McCarthy being propositioned by male and female puppet prostitutes.

Sesame Workshop said it learned of the trailer two weeks ago and asked that the tagline be removed but was rebuffed.

“We were surprised and disappointed that ‘Sesame Street,’ a show dedicated to educating young children, is being exploited to market this R-rated film,” Sesame Workshop said.

“Sesame Street,” which debuted in 1969, was created to reach as many children as possible with lessons about kindness, inclusion and life skills. It features a cast of colorful puppets known as Muppets, including popular characters such as Oscar the Grouch and Bert and Ernie. The show reaches a global audience of 190 million children, Sesame Workshop said.

In 2004, Walt Disney Company purchased the rights to some Jim Henson characters, such as Kermit the Frog and Miss Piggy. Sesame Workshop owns the rights to other Jim Henson characters, such as Elmo and Big Bird.

No Muppets or “Sesame Street” characters appear in the movie, STX said. It refers to the characters in its movie as “Henson puppets.”

The movie’s attempted association with “Sesame Street” by the tagline has confused consumers, the lawsuit claimed, citing tweets. One Twitter user wrote that a dream had come true because there was an “adult” version of “Sesame Street.”

Sesame Workshop said in its lawsuit it wants “corrective advertising” to “dispel the confusion” caused by the marketing campaign.

Follow Jeffery C. Mays on Twitter: @jeffcmays.