The New York chapter of the Alzheimer’s Association has turned down proceeds from a play because it’s about the mother of the charity’s honorary vice chairman Princess Yasmin Aga Khan. Page Six reported that “Private Dancer” — a new play starring and written by exotically named Sage Snakechalmer — delves into the life of Rita Hayworth (Khan’s mother), including the Hollywood star’s struggles with the bottle and Alzheimer’s. But Khan has objected to Hayworth’s depiction. The show launched Dec. 5 at the Lion Theatre on West 42nd Street with costumes by Zac Posen. Some proceeds were meant to go to the Alzheimer’s Association, but charity chiefs sent a letter to the producers on the day of the opening saying, “Given the sensitivity around Princess Yasmin, we have been approached by our national office to step away from our relationship and not to receive any proceeds from the show. We have to ask you to please remove our name from your Web site as soon as possible.” Khan cared for her mother at the San Remo on Central Park West after a judge ordered the star into her care. A show rep said, “We’re disappointed the production will not be able to fulfill its pledge to contribute to [the Alzheimer’s Association].” A rep for the organization did not return a request for comment.