I found the cause, the right bracket assembly bolted to the hood has play in it. If I push on the hood it rights itself and will close normally.

1955 312 T-Bird Warwick, NY

I am pretty sure everyone on this forum knows this, but for those who don't here's some advice.  Removing the engine from an early Tbird is something every owner dreads. Unfortunately, some jobs that on any other car could be done with the engine left in can not be easily done on these cars. The good news is removing the engine is not overly difficult. I can take my engine out and put it back in under 6 hours. One of the most troublesome jobs when removing the engine can be hood realignment. You can spend all day messing with the hood if you don't do this right. Before you unbolt the hood, drill a 1/8" hole through the hood hinge and the hood on both sides being careful not to drill all the way.  When you reinstall the hood, use two 1/8" drill bits in those holes to realign the hood as it was before. It's an old trick, but I am amazed when some don't know about it.

Yes, I agree with the drill bit alignment method. It is a surefire way of handling this. I would also add that I use an engine hoist to remove and install my hood by myself. Even with two folks, it's sketchy at best, so I am actually more confident to do it by myself this way. Just use moving blankets placed in strategic areas.

I have also made up temporary wooden dollies to hold the doors to remove and reinstall them by myself. This makes for a much easier job and gives you good control.

       A  L  A  N   F  R  A  K  E  S   ~  Tulsa, OK    

Hopefully, the hood is properly aligned before you drill the holes.

No need to remove the hood in a 55 bird. I have left the transmission in my 55 bird and removed the engine multiple times and not removed the hood by reaching over the fenders with an engine hoist.

  Vic Correnti

Same for a '57 Bird, no need to remove the hood.
Ernie