I've done a lot of research on the 1940 season over the years and I have an article from the Buffalo Evening News the next day which has more details about this crazy game:
"Registering five first downs to two for the Cards, the Lions had the statistical edge but this was only because Coach Jimmy Conzelman of the Chicago entry decided to punt on first down in the last two periods in the hope of picking up a loose ball near the enemy goal. In fact, the Cards did not try a single running play in the second half, except when the pass from center was too low to get a kick away."
So if that's true, Chicago basically punted the entire second half and ran only when the snap was bad. They only attempted 2 passes the entire game and it's quite possible those came in the first half although we probably won't ever know that.
The other crazy thing is the Lions could have potentially won this game. At one point, Dwight Sloan completed the only pass of the day by either team, a 26 yarder to Lloyd Cardwell at the Cardinals 1. Cardwell had squirmed into the end zone and Detroit argued that he was in, but the officials ruled him down at the 1. At this point, why they didn't just plunge into the line for a single yard, like so many teams usually did anyway in those days, is beyond me. Odd choice much like Seattle's decision not to run Lynch in the SB against New England. Anyway, Detroit ran a sweep and lost 6. Then Gaynell Tinsley and Conway Baker dumped Sloan for another loss of 6. On 3rd and goal from the 12, Sloan tried to pass and was interecepted by Tinsley. That was it for threats and the rest of the game was a punting duel.