The Legislature has the authority to administer oaths and subpoena witnesses and documents in order to obtain information about issues and problems to be addressed through legislation. Such investigations may be conducted jointly by both houses, or by a single house or single committee within either house.
Additionally, the House of Representatives has the power to impeach state judges all the way up to the Texas Court of Criminal Appeals and the Supreme Court of Texas, as well as executive branch officials.
The impeachment process is the first step in prosecuting a state official for crimes and offenses, much like an indictment in criminal courts. This step simply seeks to confirm that the charges brought against an individual have merit. If the House does impeach an official (i.e., finds sufficient cause for the charges), the Senate then tries the case.