The wording you have is solid and covers the necessary legal ground for a standard background check authorization, but there are a few minor grammatical errors, typos, and phrasing clunkiness that should be cleaned up before you put it on your page.
Here is the polished version with the corrections built-in (such as changing “where I maybe assigned” to “where I may be assigned,” fixing a few punctuation splices, and smoothing out the flow):
I hereby authorize Gulf Personnel Services, LLC, dba Snelling Staffing Services, and its designated agents and representatives to conduct a comprehensive review of my background, causing a consumer report and/or an investigative consumer report to be generated for employment purposes.
I understand that the scope of the consumer report/investigative report may include, but is not limited to, the following areas: verification of Social Security number; current and previous residences; employment history, including all personnel files; education, including transcripts; character references; credit history and reports; criminal history records from any criminal justice agency in any or all federal, state, and county jurisdictions; birth records; motor vehicle records, including traffic citations and registration; and any other public records. I also authorize the conduct of interviews with third parties relative to my character, general reputation, personal characteristics, or mode of living.
I further authorize any individual, company, firm, corporation, or public agency (including the Social Security Administration and law enforcement agencies) to divulge any and all information, verbal or written, pertaining to me to Snelling, its agents, or clients to which I may be assigned to work. I further authorize the complete release of any records or data pertaining to me which the individual, company, firm, corporation, or public agency may have, including information or data received from other sources.
I hereby release Snelling, the Social Security Administration, and its agents, officials, representatives, or assigned agencies—including officers, employees, or related personnel, both individually and collectively—from any and all liability for damages of whatever kind which may, at any time, result to me, my heirs, family, or associates because of compliance with this authorization and request to release.
*Criminal background checks will be conducted for all applicants. Credit history reports will only be generated and considered if requested by a specific client.
By checking this box, I explicitly authorize Snelling Staffing and its designated screening agencies to conduct a criminal background check and history verification. I understand that this screening may include a review of local, state, and federal criminal records. I fully release Snelling Staffing, its representatives, and any law enforcement or repository agencies from any and all liability or damages associated with the release or use of this information in connection with my application. I have read and agree to these terms.