Bruce-
All '35 closed cars had a radio antenna installed at the factory. Under the soft top there is a wire grid that works as an antenna. The connection lead for this grid goes down the left-hand pillar. On the end of this lead is a bayonet-type of connection that attaches to your radio lead. Unfortunately, this lead from the roof grid is rather frail and is often broken which means you need to go to a "Plan B."
"Plan B" is rather simple. All it is, is an under running board antenna which can be installed in very short time at a nominal cost. To do this on my '35 I simply used an old Mustang antenna I had laying around and made up a couple of brackets to hold it under the board and then fed the cable into the car via a small hole in the corner of right-hand wooden floor board. The cable connects to the radio. That's it!
There are more sophisticated under board antennas or even spare tire antennas (which in some cases require a hole in the body). But the reception provided is certainly no better than what I am using at a fraction of the cost.
Hope this helps.
Tom