Rolling resistance depends much more on the tread, the shape of a tire, and the suppleness of its side walls. A few points to explain this:
A tire with a very pronounced tread will roll less smoothly over hard roads and requires more energy than a slick tire of same width.
A ballooning tire that is considerably wider than the rim will have to deform more as it rolls.
A stiff tire dissipates more energy for these deformations.
If you like to reduce rolling resistance, you might try to get a slick tire, or a tire with small treads. (There is by the way no aquaplaning concern with slicks for bicycles.) This will bring by far the greatest gain you may get. Marginal improvements may be had if you get a tire that is only slightly wider than the rim and is supple. However, the trade-off for the latter are a higher risk of flats, less comfort, and considerably higher costs per tire.
Also note, in general a tire that is narrower has to be used with higher pressure in order to avoid pinch flats.
If you like to calculate how much a reduction of rolling resistance may bring in a best-case scenario you could use this calculator. Enter your weight desired power. Also increase the cross sectional area to something closer to 0.7 m^2 to reflect the more upright posture on a hybrid. The rolling resistance coefficient 0.004 assumes very well running tires. Calculate the speed once with this value, then double and tripple it.
Example calculation: For 100 kg weight, at sea level on a flat, and 200 W power I get 9.15 m/s, 8.53 m/s, and 7.82 m/s for coefficients 0.004, 0.008, and 0.012, respectively. For lighter riders rolling resitance matters less.
Sheldon Brown, tread patterns
ibid, tire width and pressure
Jan Heine, suspension losses