In most instances there is no tax credit for tutoring. The only exception would be in the case of a medical doctor who prescribes tutoring as treatment to a child for a diagnosed medical condition, such as ADD or ADHD, in which case the instructor would have to be certified to treat that specific condition and work in conjunction with a psychologist.
If you are completing IRS Form 2441, Child and Dependent Care Expenses, the instructions specifically state, “…do not include any expenses for sending your child to an overnight camp, summer school, or a tutoring program.” If you or your accountant are confused about this point of the tax code we recommend contacting the IRS at (800) 829-1040 to speak directly to an IRS agent to verify the statute.
The relevant IRS publications covering this matter are Publication 970 (tax benefits and credits for education), Publication 519 (miscellaneous deductions), and Publication 502 (medical and dental expenses), which are all available from the IRS website (off-site link).