Herald
was unable to find any record of the pair living in the resort town.
Surveillance video footage posted on YouTube by the Jackson police showed two people taking the American and Wyoming flags from outside the Jackson courthouse in the early hours of March 20, the
Jackson Hole News and Guide
reported.
The flags were flying at half-mast on the night of a funeral for a soldier from Evanston, Wyoming.
Tips from people who viewed the surveillance footage led the Jackson police to Mr Knapp's MySpace webpage.
Sergeant Scott Terry said Mr Knapp had yet to respond to police emails, and employers listed on his webpage had been contacted.
Viewers of the surveillance footage were scathing of the pair in comments posted on the site.
A friend of the soldier killed said: "I can't believe somebody would be so freakin' childish to do such a thing. I feel so bad for [the soldier's] wife and newborn baby."
Jackson police believe the two men have returned to New Zealand since the incident and are asking anyone who has contact with them to report it.
Watch surveillance footage of the theft below