As everyone else mentioned, as the owner of the property, you are responsible for the payment of the property taxes. You need a real estate agent who can help you determine how much rental income you can receive for the home you are interested in. This is critical information in your decision to purchase the property or not. I own several rental properties myself and can help you find a property that will provide a sufficent income in the unit you aren't living in. I can also help you list it and secure a quality tenant. Call me at 832-285-2865.
Well- as the owner, you have to pay all the taxes. Taxes are paid in arrears- so this year's taxes are payable by the end of next Jan. You want to make sure you are charging enough rent to cover the mortgage, interest, taxes and insurance, as well as regular upkeep on the property. You can look on HCAD.org to see how much your taxes are and divide by 12 to get the monthly amount. Your lender can up an escrow account if you want this money automatically added to your loan payment- that way it's put away and there's no risk of spending it!
As the property owner - you are responsible for paying all taxes on the property. The renter or tenant only pays rent and utilities -or whatever your lease agreement states. As the owner/landlord of the property - you should be able to charge a monthly rental fee adequate to pay your mortgage and property taxes. If the rents in the area are not adequate to cover your expenses - this would not be a very good investment.
Your lender will provide you with a GFE, and/or a financing worksheet, that outlines the impact the taxes have on your PITI.
When you lease out one side of the duplex it is very likely that the rent rate charged will be sufficient to cover your PITI on the rental side of the property; and perhaps a bit of profit to offset your PITI on your homestead side. Your Realtor can provide you with a CMA for the rents in the area for properties like the one you are considering.
Discuss this with your lender, and ask for a worksheet that breaks down the costs for you.