Governors voted by 11-7 with one abstention to seek approval from parents to opt out of local authority control.
Just last month, the school was highlighted by Chris Woodhead, the chief inspector, as one of 32 outstanding secondaries in the country - and one of only eight in the North. Its proposal to opt out comes as national levels of schools considering GM status have reached an all-time low.
Since September and John Major's opt-out drive, twice as many secondary schools have rejected opting out as have voted for it. In the past five months, five secondary schools have voted yes, but 12 have said no. In the primary sector, 16 schools have backed GMS and 11 rejected it.
GM supporters believe that opt-out approval for Harrogate grammar would have a domino effect in North Yorkshire, which has only one opted-out school - Nun Monkton, near York.
But both Cynthia Welbourn, who will be North Yorkshire's education director from April, and Kevin McAleese, Harrogate grammar's head, are unsure.
Seven North Yorkshire schools have already rejected GMS. Three are in Scarborough, along with Woodlands in Harrogate, Ripon grammar, Norton secondary and Romanby primary in Northallerton.
Miss Welbourn said: "It is very difficult to say whether others will follow Harrogate grammar if it goes. Since the school announced it was going to hold a ballot, there has been very strong reaction from other secondary heads in the area who are very committed to maximum delegation but also local partnership.
"Harrogate grammar is an excellent school, but it is one of a lot of excellent schools in North Yorkshire."
Mr McAleese added: "North Yorkshire is a very diverse LEA with secondary schools of every type. I would be surprised if there were a domino effect. "
Despite its name, Harrogate grammar is a comprehensive, although its intake is skewed towards high achievers.
It is oversubscribed, with 350 applications for 246 places. Last year's results at the 1,600-pupil school were twice the national average - 82 per cent gained five GCSEs grades A-Cs - and 13 pupils gained Oxbridge places.
Mr McAleese said earlier this month that he would consider more selection on ability to do "what was best for the school".