From the beginning of the closed-bodied cars designs in the early 1920s, car makers sought after an all steel roof.  Early attempts with boxy cars of the time failed, because of air turbulence drumming of the top panel.  As long as flat car tops remained, their could be no solid steel roof, even if one could have been manufactured.  By the early 1930’s roof designs began to change with a much more curved structure.

In 1932, Inland Steel opened the first continuous sheet mill capable of making wide sheet metal and at the same time the steel industry created steel formulations which allowed deep-draw stamping for the first time, thus creating opportunity to make a single piece roof with enough crown to avoid the dreaded drumming effect.

The first all steel tops, appeared on all 1935 GM cars as the Fisher Body “Turret Top”.  At least one source I found on the internet indicated this happened in 1933 with Oldsmobile sedans and coupes, but my research in looking at the 1933/1934 sales brochures for Oldsmobile confirms this is not true.

Studebaker used an all one piece steel top for both Dictator’s and Presidents in 1936.

Ford was one of the last to change over, doing so in 1937.  By then almost all the car manufactures except those with limited production, such as the “Senior Packard’s” had made the change.

Side Bar:  Yes, there were very high end automobiles made with solid steel roofs, earlier then the 1935 GM cars, but they were not made as one continuous steel part, but were rather manufactured from several smaller panels and welded together.