There are typically three types of petitions utilized by Citizens for redress of grievances with their government.
1.  Initiative - "to initiate a new law"
2.  Referendum - "to reform an existing law"

3.  Recall - "to recall and remove an elected official from office"

Texas state law does not grant these rights of petition at the state level.  The only residents who have these petition rights are individuals who live in municipalities with populations of 5,000 or more and who have a Home Rule City Charter that specifically grants these rights to their residents through Texas Local Government Code 9.004 .