Nonpotential characteristics of magnetic fields in AR 5747 are examined using Mees Solar Observatory magnetograms taken on Oct. 20, 1989 to Oct. 22, 1989. The active region showed such violent flaring activities during the observational span that strong X-ray flares took place including a 2B/X3 flare. The magnetogram data were obtained by the Haleakala Stokes Polarimeter which provides simultaneous Stokes profiles of the Fe I doublet 6301.5 and 6302.5. A nonlinear least square method was adopted to derive the magnetic field vectors from the observed Stokes profiles and a multi-step ambiguity solution method was employed to resolve the $180^{circ}$ ambiguity. From the ambiguity-resolved vector magnetograms, we have derived a set of physical quantities characterizing the field configuration, which are magnetic flux, vertical current density, magnetic shear angle, angular shear, magnetic free energy density, a measure of magnetic field discontinuity MAD and linear force-free coefficient. Our results show that (1) magnetic nonpotentiality is concentrated near the inversion line in the flaring sites, (2) all the physical parameters decreased with time, which may imply that the active region was in a relaxation stage of its evolution, (3) 2-D MAD has similar patterns with other nonpotential parameters, demonstrating that it can be utilized as an useful parameter of flare producing active region, and (4) the linear force-free coefficient could be a evolutionary indicator with a merit as a global nonpotential parameter.