You can use an extremely wide (pardon the pun) variety of tire widths on any given rim. There would be no problem at all running anywhere from 28-38mm on your current wheel. If your rims are wider than a standard road rim (just roll your bike up next to a road bike and take a look) then I wouldn't go any narrower than 28. Why? Because the tire profile would get flattened out too much and cause your bike to handle funny. On the other extreme I wouldn't go past about 44mm - too wide and you might have the tire roll off the rim and you probably couldn't get the wheel back on your bike anyway.