GRB 250306***A***, Swift-BAT refined analysis S. D. Barthelmy (GSFC), R. Gupta (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), D. Sadaula (GSFC/UMBC), T. Sakamoto (AGU) (i.e. the Swift-BAT team): Using the data set from T-240 to T+200 sec from the recent telemetry downlink, we report further analysis of BAT GRB 250306***A*** (trigger #1293340) (NAME, et al., GCN Circ. xxxx). The BAT ground-calculated position is RA, Dec = 354.724, -47.998 deg which is RA(J2000) = 23h 38m 53.7s Dec(J2000) = -47d 59' 52.5" with an uncertainty of 1.1 arcmin, (radius, sys+stat, 90% containment). The partial coding was 13%. [Description about the mask-weighted light curve] T90 (15-350 keV) is 11.4 +- 2.4 sec (estimated error including systematics). The time-averaged spectrum from T-1.5 to T+19.0 sec is best fit by a power law with an exponential cutoff. This fit gives a photon index 0.88 +- 0.24, and Epeak of 133.7 +- 47.2 keV (chi squared 65.07 for 56 d.o.f.). For this model the total fluence in the 15-150 keV band is 8.9 +- 0.3 x 10^-06 erg/cm2 and the 1-sec peak flux measured from T+0.14 sec in the 15-150 keV band is 35.7 +- 1.6 ph/cm2/sec. A fit to a simple power law gives a photon index of 1.37 +- 0.06 (chi squared 78.10 for 57 d.o.f.). All the quoted errors are at the 90% confidence level. The results of the batgrbproduct analysis are available at http://gcn.gsfc.nasa.gov/notices_s/1293340/BA/