GRB 210419***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-239 to T+963 sec from the recent telemetry downlink, we report further analysis of BAT GRB 210419***A*** (trigger #1044236) (NAME, et al., GCN Circ. xxxx). The BAT ground-calculated position is RA, Dec = 212.961, 35.995 deg which is RA(J2000) = 14h 11m 50.7s Dec(J2000) = +35d 59' 43.0" with an uncertainty of 1.7 arcmin, (radius, sys+stat, 90% containment). The partial coding was 71%. [Description about the mask-weighted light curve] T90 (15-350 keV) is 54.5 +- 12.0 sec (estimated error including systematics). The time-averaged spectrum from T+12.0 to T+88.8 sec is best fit by a simple power-law model. The power law index of the time-averaged spectrum is 2.43 +- 0.26. The fluence in the 15-150 keV band is 7.8 +- 1.2 x 10^-07 erg/cm2. The 1-sec peak photon flux measured from T+47.97 sec in the 15-150 keV band is 0.8 +- 0.2 ph/cm2/sec. 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/1044236/BA/