Simple answer: no, you do not withhold taxes. The IRS Household Employer’s Tax Guide does not treat a tutor as a household employee, even when the tutoring is done in the home.
But, as others have said, it's not clear cut. The most important thing is to discuss taxes with the tutor, so that there is an understanding of who is responsible for taxes. One theory says you should offer to pay him 7% more if he files as an independent contractor to cover the "employer share of FICA (social security & Medicare tax)
