GRB 130508***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-723 to T+963 sec from the recent telemetry downlink, we report further analysis of BAT GRB 130508***A*** (trigger #555413) (NAME, et al., GCN Circ. xxxx). The BAT ground-calculated position is RA, Dec = 305.355, 34.977 deg which is RA(J2000) = 20h 21m 25.2s Dec(J2000) = +34d 58' 38.5" with an uncertainty of 1.9 arcmin, (radius, sys+stat, 90% containment). The partial coding was 60%. [Description about the mask-weighted light curve] T90 (15-350 keV) is 42.9 +- 10.1 sec (estimated error including systematics). The time-averaged spectrum from T+10.2 to T+58.7 sec is best fit by a simple power-law model. The power law index of the time-averaged spectrum is 1.85 +- 0.25. The fluence in the 15-150 keV band is 6.1 +- 1.1 x 10^-07 erg/cm2. The 1-sec peak photon flux measured from T+11.05 sec in the 15-150 keV band is 0.6 +- 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/555413/BA/