Look for the sticker on your rims. It might give the actual measurement ... something like 622 x 20. My Fisher Hybrid came with Matrix 550 rims that size. Sheldon Brown (at http://www.sheldonbrown.com/tire-sizing.html) suggests 21 width rims could take a tire as small as 35mm and 19mm rims a tire as small as 28. Maybe a 20 could hold a 32mm tire safely.

In any event you need to figure out your actual rim width to decide which tire you could try.

Good Luck!