I decided I'd take my laundry over to the corner laundromat and that while I was doing that I'd look around to see if there was any obvious source for the gas fumes. None of the nearby cars had any puddles of gas under them or anything, though, and in fact the smell seemed to pretty much disappear as soon as I went outside. (Actually, the smell seemed strongest in the stairwell outside my apartment.)
When I went back to my apartment I observed that the smell became very strong as soon as I entered the building. I decided to go up to the third floor apartment to see if they were also experiencing it and if so if they had any idea what its source might be.
In the stairwell outside the third floor apartment I found a collection of various items, including an open gas can. This I removed and put outside on the second-floor porch, leaving a note explaining that I had done so because I was worried about the fumes.
The gas can is now gone and so are the fumes. It's very nice.