Mostly not a deduction. Read the bottom for a list of things that are deductible when you buy a house. If you rent 1/3, then 2/3 of those costs are itemized deductions on schedule A, and 1/3 are rental expenses.
The rest of your costs are totaled up and added to the purchase price and considered part of your cost basis. You can take 1/3 of the cost basis as your basis for depreciation and take a depreciation deduction over 27-1/2 years.
Most closing costs are not deductible. Instead, they are added to the cost of the house and may reduce your capital gains when you sell. These closing costs are deductible in the year you closed:
1. Daily mortgage interest from the day you closed to the end of the month. Shown on your closing document, you may not get a 1098 for this.
2. Property taxes. Generally, the seller has prepaid a year's worth of property taxes and you will give a credit to the seller for the amount of tax that is allocated to the days you will own the home. That property tax credit is deductible as if you paid it directly to the city or county.
3. Mortgage insurance premiums. If you paid a lump sum premium for mortgage insurance from the VA or the Rural Housing Authority (called a funding fee) that is deductible in the year you close. Other lump sum mortgage insurance premiums must be spread out over 84 months and deducted when you make your monthly mortgage payment. Your bank is supposed to put allocated lump sum PMI on the 1098 but not all do. If your bank did not, you can enter the premiums yourself. Be aware that turbotax does not keep track of the 84 month deduction, you need to do that yourself. And the mortgage insurance deduction also has an income limit so not every one will qualify.
4. Mortgage "points." Origination fees or points are considered a form of mortgage interest and must be deducted over the life of the loan, unless you meet certain tests. If you paid points, turbotax will ask you questions to see if you can deduct them all at once (in the year you closed) or if you have to spread them out. Origination fees are considered points if they are a percentage of the loan amount (not a flat fee) and if they are not assigned to any specific services like document processing, attorney fee, or other specific costs.