As an employer - you generally need to do withholding according to W-4 form provided by the employee.
Employees may change W-4 any time and it will be in effect from that point forward - but changes may not be made retroactively. Do not adjust withholding retroactively!
Employees may claim a refund on their tax returns.
Withholding errors made by an employer are to be corrected.
If you filed form 941 - http://www.irs.gov/pub/irs-pdf/f941.pdf - and discover an error on a
previously filed Form 941, make the correction using Form 941 for the quarter in which you discovered the error and attach Form 941c, Supporting Statement to Correct Information - http://www.irs.gov/pub/irs-pdf/f941c.pdf