You should consult a tax professional to ensure your taxes are handled appropriately. This forum is geared towards Real Estate questions. Best of Luck!
I am not sure if you are asking about Texas property taxes or Texas income taxes. Texas does have property taxes on real estate you own, but does not have a state income tax. If you do not own property, you do not owe state or local taxes to the State of Texas. If you closed on a property on 12/18/2015, the title company would have collected the prorated portion of property taxes from the seller up until the closing date. They would credit these to you and have you pay the pro-rated portion for the time you owned the property up to the end of the year. The title company likely would have paid the 2015 property tax bill for you out of the closing proceeds. I hope this answers your question.