My first thought is call a major museum and ask them where to take it for authentication. Then I googled!
there is a gallery called Questroyal Fine Art with branches on 5th ave and in Brooklyn that deals in 19th century and early 20th century American artists. I also found that Hal Robinson did a lot of his work in Old Lyme Ct. So it seems that a dealer or museum in Old Lyme might be able to give you the info you want.
Congratulations....the bug has bitten! Linda C

I checked him out on Askart.com. He wasn't a Hudson River school painter, although your painting could be of the Hudson River Valley. As Linda said, he was associated with Old Lyme, and he worked primarily in the early 20th century. For $13.50, you can get 24-hour access to Askart, which is a database of artist info and auction records. It shows images and auction sale price for many Hal Robinson paintings, so you could see if yours resembles those. It also shows a sample of his signature. Your local public library may also have a reference book that shows artist signatures, and they may have access to auction records.