It's a Jimdandy ratrod grille. Do I get full points for that guess?
Anyhow I went out and looked at my stash and the '34 truck Dodge Brothers has a rounder bottom on it and my '33 Plymouth has no grille shell and the grille bars bulge out just below the top. The little strips that hold the grille bars apart look like 1/4" channel with hacksaw cuts in them to hold both sides of each bar; on both grilles. If you look on Alumicraft or some of the businesses that make new grilles you might see the grille shell you have. I think it is a '34 Dodge Brothers car.
Found a similar grill for sale online and this is what's wrote...
"Rockne automobiles were produced for a very short time by Studebaker Co. which makes this grill a rare item. It is similar in size to other grills made in 1934."