2003 trailblazer back air stays on after the truck is turned off

Hi, there is a technical service bulletin published by general motors about these trailblazers and this problem, it is very common to have this problem if you own one of these. the rear a/c module is located on the passenger side in the very back underneath the plastics and bezels in the back. there is a blower resistor module that controls the fan speeds and recieves input from the control panel that gets too hot and melts the plastic surrounding the wiring connector and allows the terminal inside the connector to short the fan control wire to battery power. if this is the case, you will have to replace the resistor module, the wiring and connector, and sometimes the blower motor. you should contact you local gm/chevy dealer for parts though, they have the wiring pigtail so you replace just the connector end, and the new style resistor module, and if i remeber right, i think there is a air shield in the kit to install to improve air flow inside across the resistor to help cool it down. the blower motor when running produces the cooling ability for the resistor, if there was no airflow across the resistor, it would overheat almost immeadiatly. take the rear plastics off and the rear seat out, and have a look, you should be able to find this problem pretty quickly.