Looked up the details for Texas and for what we would likely call a cigar it is 1.1 cents each.
This is the direct link to the Texas cigar tax law (in HTML).
From a general tax perspective, there is no state income tax and the state sales tax is 6.25%. In Houston proper the local sales taxes add 2% more for 8.25% total.
For anyone interested here is a direct link to the SCHIP law (in PDF).