By Richard Weizel

MYSTIC, Connecticut (Reuters) - A playground honoring a 7-year-old victim of the Sandy Hook School massacre in Connecticut was vandalized by a man who told the girl's mother in a phone call just days before Mother's Day that the shootings were a "hoax" and her daughter never existed, authorities said on Wednesday.

Police are investigating the theft of a 50-pound vinyl sign from a playground in Mystic, Connecticut, dedicated to first-grader Grace McDonnell, who was gunned down with her classmates in 2012.

"It's sick that some people would do something this horrific to a family already so traumatized," said Bill Lavin, who is organizing the effort to build 26 playgrounds to commemorate the 20 children and six adults killed in the shooting spree on December 14, 2012.

Gunman Adam Lanza, 20, a former student at Sandy Hook, also killed his mother the same day and shot himself to death in one of the worst school shootings in U.S. history.

The theft in Mystic marked the second act of vandalism at Connecticut playgrounds honoring Sandy Hook victims. Just days earlier, vandals spray-painted graffiti on a sign at a playground in Hartford that is dedicated to first-grader Anna Grace Marquez-Greene.

The sign in the Mystic playground named to honor Grace McDonnell on April 27 included a peace symbol based on her artwork.

Its theft touched a nerve across the United States, said Lavin, founder of the Where Angels Play Foundation, a New Jersey non-profit organization building the playgrounds in Connecticut, New York and New Jersey.

"We've been getting calls from people around the country who are outraged and have already sent enough in donations that we will put up more signs and billboards with the message to 'Live Grace-Fully' in honor of Grace," Lavin said.

Lavin said the vandalism was discovered after the man phoned Lynn McDonnell, Grace's mother, early last week "to tell her he took the sign because it was all a hoax."

McDonnell could not be reached for comment. Lavin said she was "obviously very upset" and the family has asked the foundation to address all media inquiries about the sign theft.

Nearly all of the 26 playgrounds have been opened, with plans to dedicate the 22nd one to slain pupil Benjamin Wheeler on Sunday in Ocean City, New Jersey. The final playground will be opened by August and dedicated to the school's late principal Dawn Hochsprung, among the first victims killed by Lanza.

"This isn't going to stop us from moving forward. We will replace the sign and move ahead," Lavin said.

(Editing by Barbara Goldberg and Leslie Adler)