Now this was back in 1988 during the 333 strike but I was told that I had to file in N.Y. State as that was where my company was located. After I got the first check I could then transfer my claim to my home state Florida. I was paid the N.Y. rate even though FL was much lower.
Not sure how it works now but from what I have been told by some friends down here in FL (landlubbers) that it is all done on line.