Chapter 12-2 of the Skydiver’s Competition Manual has instructions for establishing state and national records. Appendix B, the claim form, is available for download to the right. A summary:
State records: You’ll need the jump(s) observed by at least one discipline-specific judge (for example, you need a FS judge to grade a 4-way sequential record attempt) plus one other qualified person listed in Chapter 12 (also listed on the claim form). You only need two authorized signatures to confirm a state record, and your judge can take part in the jump!
National records: For national performance record attempts made outside of a USPA National Championships (for example, a large formation FS record attempt) you’ll need three judges, at least two of them nationally-rated in the discipline involved. One observer can be a judge with a regional rating. For video graded records, only one of the three judges need actually be on site to collect the video; the judging can be done remotely.
Altitude jumps and most-jumps-in-24 hours claims: You don’t need a judge, although using a judge as an official observer is perfectly acceptable. However, if you’d rather, the pilot’s signature and one other qualified observer (as listed in Chapter 12 and the record claim form) will satisfy the requirement.