Here's where it can get really obscure. Grease was Tony-eligible because it was produced under the Production contract which is the one that Broadway shows are produced under. (Some are done under a LORT contract now.) The theatre it opened in was the Eden (soon-to-be-Entermedia and now the Village East 7-plex movie theatres) at 2nd Avenue and East 12th Street. The capacity of the theatre was about 1100 then.
Tony-eligible is usually by theatre and/or contract. Hence the Beaumont which uses the LORT contract for the first 10 weeks of the run and if business warrants must switch to the Production contract, is still an eligible house. Back in 1972 the Eden/Entermedia was on the eligible list. By 1981 or so with Joseph... I'm not sure it was on the list any more.
I told you it was obscure.
NB-History Time: Before becoming the Eden in 1969 or so for the original run of Oh, Calcutta (non eligible, I believe), this same theatre was the Casino East for a long run of an old fashioned burlesque show starring a slightly-long-in-the-tooth, former strip queen named Ann Corio called This Was Burlesque and before that was the Phoenix, home of the famed and legendary Phoenix Rep Company where Once Upon a Mattress and The Golden Apple among many many others, originated. It was built as one of the Yiddish theatres that flourished on lower 2nd Avenue. Indeed if you go into what is called Theatre #1 which is pretty much all of the Mezzanine and the front of the orchestra of the original theatre, you will see the landmarked ceiling which has a huge Star of David inlaid into the dome.
"If my life weren't funny, it would just be true. And that would be unacceptable."
--Carrie Fisher