Below is a link to the official State of Texas site on how to elect to avoid the vaccinations due to religious or philosophical objections. It clearly outlines what a parent must do in order to opt out of vaccinations in Texas. Each state is different and we must know what is required rather than generalities.
Here's a sample http://www.dshs.state.tx.us/immunize/docs/sample_letter.pdf of the initial "exemption from Immunizations Conscience form which should be completed and then either mailed or FAXED to the address indicated on the form. The Department of State Health Services will then type up an official exemption form which will be mailed to you , needs to be notarized and then given to the child's school.