By population, Houston is the largest city in Texas. It makes sense that Houston has the highest death rate in the state.
The statistics show that about 150,000 to 200,000 Texas residents die each year. They also show that 18,000 to 28,000 of these residents lived in Harris County. For example, in 2014, 24,000 residents of Harris County died. That averages out to 2,000 deaths per month.
There are several cities and municipalities that are in Harris County that are not part of Houston. If you look just at Houston deaths, they range from 12,000 to 17,000 a year. The 2014 data shows 15,000 deaths in Houston. That is more than 1,000 per month.