Comedian Saget was found dead in a hotel room in Florida on 9 January. He was 65 years old.
Making this request, Saget's family have said that the evidence collated at the scene of his death depicted him "graphically" and should not be released to the public or media.
Legal documents have asked for an injunction that will prevent sensitive information being released to anyone, except for family members.
The lawsuit was brought on behalf of Saget's wife Rizzo and their daughters against the Orange County Sheriff's Office and the Medical Examiner's Office. They have also shared the investigations made by police following Bob Saget's death.
The documents have stated, "In the process of these investigations, defendants created records which include photographs, video recordings, audio recordings, statutorily protected autopsy information, and all other statutorily protected information".
"Upon information and belief, some of these records graphically depict Mr Saget, his likeness or features, or parts of him, and were made by defendants".
"Upon information and belief, certain news and media outlets have filed or plan to file public records requests... requesting defendants release the records to the public".
The lawsuit has also added that the "unjunctive relief" was necessary for protecting the family's "legitimate privacy interests".
It also added, "For the reasons stated herein, plaintiffs seek a temporary and permanent injunction precluding defendants from releasing the records to anyone except plaintiffs as the surviving spouse and daughters of Mr Saget, or to plaintiffs designee".
