First, a withdrawal from a 401k account cannot be used for a home purchase to be exempt from the 10% early withdrawal penalty. That is only available if the funds were withdrawn from an IRA and then only the first $10,000 is exempt from the penalty. See this IRS Tax Topic on non-IRA withdrawals and the penalty - https://www.irs.gov/taxtopics/tc558.html
Second, the withdrawal is a taxable event and is included on your tax return as ordinary income taxed at your current tax rate. Additionally, if you were under the age of 59 1/2 or if you have separated from the service of the employer and under the age of 55 at the time of the withdrawal then a 10% early withdrawal penalty will be assessed on your federal tax return as a tax liability. Any taxes withheld on the withdrawal will be entered on your tax return as a tax payment (just like from a W-2)
