There were two people named James Arnett who were born in Ohio in 1930's.
1940 US Census, Barberton, Summit Co., OH familysearch.org/pal:/MM9.1.1/KWLB-823
1940 US Census, Columbus, Franklin Co., OH familysearch.org/pal:/MM9.1.1/KW8Z-S5T
The other James Arnett's in OH seem to have a middle name or middle initial.
Do you have any other facts to help sleuth out more answers?