GRB 250603***A***, Swift-BAT refined analysis S. D. Barthelmy (GSFC), R. Gupta (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), D. Sadaula (GSFC/UMBC), T. Sakamoto (AGU) (i.e. the Swift-BAT team): Using the data set from T-240 to T+962 sec from the recent telemetry downlink, we report further analysis of BAT GRB 250603***A*** (trigger #1320335) (NAME, et al., GCN Circ. xxxx). The BAT ground-calculated position is RA, Dec = 129.947, -39.309 deg which is RA(J2000) = 08h 39m 47.4s Dec(J2000) = -39d 18' 32.8" with an uncertainty of 2.0 arcmin, (radius, sys+stat, 90% containment). The partial coding was 77%. [Description about the mask-weighted light curve] T90 (15-350 keV) is 15.7 +- 11.9 sec (estimated error including systematics). The time-averaged spectrum from T-13.9 to T+15.8 sec is best fit by a simple power-law model. The power law index of the time-averaged spectrum is 1.78 +- 0.30. The fluence in the 15-150 keV band is 3.6 +- 0.7 x 10^-07 erg/cm2. The 1-sec peak photon flux measured from T+0.14 sec in the 15-150 keV band is 1.3 +- 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/1320335/BA/