GRB 240309***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 240309***A*** (trigger #1219325) (NAME, et al., GCN Circ. xxxx). The BAT ground-calculated position is RA, Dec = 299.813, 35.157 deg which is RA(J2000) = 19h 59m 15.0s Dec(J2000) = +35d 09' 26.2" with an uncertainty of 1.4 arcmin, (radius, sys+stat, 90% containment). The partial coding was 85%. [Description about the mask-weighted light curve] T90 (15-350 keV) is 133.26 +- 31.91 sec (estimated error including systematics). The time-averaged spectrum from T-59.42 to T+127.53 sec is best fit by a simple power-law model. The power law index of the time-averaged spectrum is 1.74 +- 0.09. The fluence in the 15-150 keV band is 4.0 +- 0.2 x 10^-06 erg/cm2. The 1-sec peak photon flux measured from T-51.80 sec in the 15-150 keV band is 0.7 +- 0.2 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/1219325