GRB 210306***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), D. M. Palmer (LANL), T. Parsotan (GSFC/UMBC), T. Sakamoto (AGU), M. Stamatikos (OSU) (i.e. the Swift-BAT team): Using the data set from T-240 to T+892 sec from the recent telemetry downlink, we report further analysis of BAT GRB 210306***A*** (trigger #1035994) (NAME, et al., GCN Circ. xxxx). The BAT ground-calculated position is RA, Dec = 129.964, 60.203 deg which is RA(J2000) = 08h 39m 51.3s Dec(J2000) = +60d 12' 11.2" with an uncertainty of 1.0 arcmin, (radius, sys+stat, 90% containment). The partial coding was 53%. [Description about the mask-weighted light curve] T90 (15-350 keV) is 637.3 +- 34.9 sec (estimated error including systematics). The time-averaged spectrum from T-0.2 to T+735.0 sec is best fit by a power law with an exponential cutoff. This fit gives a photon index 0.60 +- 0.60, and Epeak of 54.8 +- 10.2 keV (chi squared 41.02 for 56 d.o.f.). For this model the total fluence in the 15-150 keV band is 4.9 +- 0.5 x 10^-06 erg/cm2 and the 1-sec peak flux measured from T+7.50 sec in the 15-150 keV band is 20.8 +- 0.7 ph/cm2/sec. A fit to a simple power law gives a photon index of 1.74 +- 0.11 (chi squared 54.89 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/1035994/BA/