GRB 240306***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-60 to T+243 sec from the recent telemetry downlink, we report further analysis of BAT GRB 240306***A*** (trigger #1218903) (NAME, et al., GCN Circ. xxxx). The BAT ground-calculated position is RA, Dec = 299.241, 35.412 deg which is RA(J2000) = 19h 56m 57.8s Dec(J2000) = +35d 24' 42.6" with an uncertainty of 2.9 arcmin, (radius, sys+stat, 90% containment). The partial coding was 45%. [Description about the mask-weighted light curve] T90 (15-350 keV) is 6.66 +- 3.19 sec (estimated error including systematics). The time-averaged spectrum from TTBD to TTBD sec is best fit by a simple power-law model. The power law index of the time-averaged spectrum is 0.00 +- 0.00. The fluence in the 15-150 keV band is 5.2 +- 1.0 x 10^-07 erg/cm2. The 1-sec peak photon flux measured from T+81.66 sec in the 15-150 keV band is 0.3 +- 0.1 ph/cm2/sec. 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/1218903