Dear Mr. Bright,
Thank you for posting your request on History Hub!
We searched the National Archives Catalog and located a record series titled Appellate Jurisdiction Case Files, 1792 - 2015 in the Records of the Supreme Court of the United States (Record Group 267). For access to these records, please contact the National Archives in Washington, DC - Textual Reference (RDT1) via email at firstname.lastname@example.org.
We also searched online and were able to locate a number of primary sources. The Opinion of the Supreme Court and the concurrences are available online at multiple websites. The website Oyez has both the opinions and audio recordings of the oral arguments, all of which count as primary sources Also available online is an interview of Joseph H. Rodriguez, who represented the student in this case. This would count as a primary source because he was directly involved in the case. Another primary source is the opinion of the Supreme Court of New Jersey, which heard the case in 1983 before it was appealed to the Supreme Court of the United States.
Another category of primary sources would be contemporary newspaper articles reporting on the case and newspaper editorials reacting to the case. Your local library may have copies of newspapers from this time period. Also, The Library of Congress website Chronicling America has a U.S. Newspaper Directory that may be useful in locating newspapers from this time period.
One helpful secondary source is the Facts and Case Summary - New Jersey v. T.L.O. page on the website of the United States Courts.
We hope this information is helpful. Best of luck with your research.