GRB 240303***A***: Swift-BAT refined analysis S. D. Barthelmy (GSFC), H. A. Krimm (NSF), S. Laha (GSFC/UMBC), A. Y. Lien (U Tampa), C. B. Markwardt (GSFC), M. J. Moss (GSFC), D. M. Palmer (LANL), T. Parsotan (GSFC), T. Sakamoto (AGU) (i.e. the Swift-BAT team): Using the data set from T-239 to T+963 sec from the recent telemetry downlink, we report further analysis of BAT GRB 240303***A*** (trigger #1218452) (NAME, et al., GCN Circ. xxxx). The BAT ground-calculated position is RA, Dec = 229.772, -57.367 deg which is RA(J2000) = 15h 19m 05.4s Dec(J2000) = -57d 22' 03.0" with an uncertainty of 2.2 arcmin, (radius, sys+stat, 90% containment). The partial coding was 86%. [Description about the mask-weighted light curve] T90 (15-350 keV) is 773.17 +- 43.28 sec (estimated error including systematics). The time-averaged spectrum from TTBD to TTBD sec is best fit by a power law with an exponential cutoff. This fit gives a photon index 1.68 +- 0.51, and Epeak of 15.1 +- 11.0 keV (chi squared 69.78 for 56 d.o.f.). For this model the total fluence in the 15-150 keV band is 5.5 +- 0.4 x 10^-06 erg/cm2 and the 1-sec peak flux measured from T-80.60 sec in the 15-150 keV band is 0.4 +- 0.2 ph/cm2/sec. A fit to a simple power law gives a photon index of 2.48 +- 0.11 (chi squared 77.20 for 57 d.o.f.). All the quoted errors are at the 90% confidence level. The results of the batgrbproduct analysis are available at https://swift.gsfc.nasa.gov/results/batgrbcat/BAT_refined_circular/1218452