Political restrictions bar the incumbent from holding political office or supporting a particular political viewpoint in a public forum, and usually apply to council staff in senior or sensitive posts, such as those in media relations. Charity jobs cannot be politically restricted.
Kirklees Active Leisure, which had an income of £9.3m in 2006/07, was established by Kirklees Council in 2002 to run 10 sports centres and swimming pools. The chief executive's position was advertised in The Guardian on 4 March.
The Charity Commission received a complaint that a post in an independent charitable trust could not be politically restricted.
In a statement, the commission said: "We have contacted the charity's trustees to advise them that a charity cannot politically restrict a post, as this would be an infringement of the charity's independence, and are awaiting the trustees' comments."
Tracey Spencer Tootill, human resources manager at Kirklees Active Leisure, said the post was not politically restricted and the phrase was included in the advert because of an administrative error.
"By the time I noticed the error it was too late," she said. "Everything was printed and pulling it would have meant delaying recruitment. But we have made it clear to candidates that the position isn't politically restricted."
Kevin Curley, chief executive of Navca, said the advert, which also described the job category as "local government", called into question the independence of leisure trusts from the councils that created them.
"This is something we have always expected, but it is the most blatant example of a council treating the chief executive of a local charity as though he or she was one of its own officers," he said.
He said leisure trusts' lack of independence meant they should not get charitable status. "They shouldn't be able to compete unfairly with genuine charities," he said. "Charities should be independent."
Spencer Tootill denied there had been any infringement of the charity's independence. She said the advert had been written by the charity's chair of trustees, David Heddon, who also conducted the interviews and, with other trustees, selected the winning candidate, who will be announced this week.
She said the council had offered only general advice and supplied only one elected member to serve as company secretary on the leisure trust's board.