GRB 140304***A***, Swift-BAT refined analysis S. D. Barthelmy (GSFC), W. H. Baumgartner (GSFC/UMBC), J. R. Cummings (GSFC/UMBC), N. Gehrels (GSFC), H. A. Krimm (GSFC/USRA), A. Y. Lien (GSFC/UMBC), C. B. Markwardt (GSFC), D. M. Palmer (LANL), T. Sakamoto (AGU), M. Stamatikos (OSU), T. N. Ukwatta (LANL) (i.e. the Swift-BAT team): Using the data set from T-120 to T+1468 sec from the recent telemetry downlink, we report further analysis of BAT GRB 140304***A*** (trigger #590206) (NAME, et al., GCN Circ. xxxx). The BAT ground-calculated position is RA, Dec = 30.649, 33.473 deg which is RA(J2000) = 02h 02m 35.8s Dec(J2000) = +33d 28' 23.0" with an uncertainty of 1.0 arcmin, (radius, sys+stat, 90% containment). The partial coding was 74%. [Description about the mask-weighted light curve] T90 (15-350 keV) is 14.8 +- 1.4 sec (estimated error including systematics). The time-averaged spectrum from T-3.8 to T+13.5 sec is best fit by a power law with an exponential cutoff. This fit gives a photon index 0.85 +- 0.33, and Epeak of 136.9 +- 109.2 keV (chi squared 54.70 for 56 d.o.f.). For this model the total fluence in the 15-150 keV band is 1.1 +- 0.1 x 10^-06 erg/cm2 and the 1-sec peak flux measured from T+10.22 sec in the 15-150 keV band is 1.7 +- 0.2 ph/cm2/sec. A fit to a simple power law gives a photon index of 1.30 +- 0.08 (chi squared 60.75 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/590206/BA/