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My 1936 Oldsmobile parts book shows under group 1.516 INDICATOR, Oil Level .
Part number 392218 for model 30 E (1927) with a note saying " And air cleaner"
I can assume from this that the dipstick was attached to the oil fill cap.
And it just went directly down the oil fill tube into the crankcase.
Others may have more information. But yes, it does have a dipstick.