Lear60 Flight Crew experiences unsafe nose gear indication after retraction. Extension produces three safe indications. A tower fly by indicates the nose gear is cocked 90 degrees from normal. Upon touch down the nose gear straightens itself out and normal roll out ensues.

Narrative

We departed under FAR Part 91. After rotation and positive rate; the gear was selected 'up.' The main gear retracted properly; but the nosewheel indicated 'unsafe' with one red light. We recycled the landing gear down once; and it indicated three safe landing gear ('three green') and no red 'unsafe' lights. We were overweight for landing; so we decided to proceed on course with the gear down. At this point; we had surmised that it was a minor problem with the alignment of the nosewheel that could be fixed at the next airport; after reaching landing weight. We continued north to our destination. Upon arrival; we decided to have the Tower visually inspect our landing gear for the orientation of the nosewheel. After the first pass; they indicated the nosewheel looked off '30 or 40 degrees.' We did another low approach; and they then indicated it appeared to be turned '90 degrees; perpendicular to the longitudinal axis.' After this; we went offshore a few miles and orbited in VMC conditions while we ran various checklists; spoke with the Director of Operations and Maintenance Technicians; and executed some troubleshooting procedures. After we tried several procedures; we executed another low approach. They said the orientation of the nosewheel had not changed. We then went out over the water again and orbited. We briefed the passengers for an emergency landing and evacuation (if necessary); briefed the landing among the crew; declared an emergency; and told Tower of our intentions to make an emergency landing with the nosewheel turned 90 degrees. We flew a normal approach. I landed the aircraft nose-high and gently lowered the nosewheel. Upon nosewheel touchdown; the wheel abruptly turned to its normal forward position; and the rest of the rollout and taxi-off went without incident. Besides the abrupt nosewheel correction during rollout; the landing was safe without damage to the aircraft. No passengers or crew were injured.