GRB 060604***A***, Swift-BAT refined analysis S. D. Barthelmy (GSFC), 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-239 to T+843 sec from the recent telemetry downlink, we report further analysis of BAT GRB 060604***A*** (trigger #213486) (NAME, et al., GCN Circ. xxxx). The BAT ground-calculated position is RA, Dec = 337.242, -10.905 deg which is RA(J2000) = 22h 28m 58.1s Dec(J2000) = -10d -54' -18.0" with an uncertainty of 2.5 arcmin, (radius, sys+stat, 90% containment). The partial coding was 72%. [Description about the mask-weighted light curve] T90 (15-350 keV) is 96.0 +- 22.6 sec (estimated error including systematics). The time-averaged spectrum from T-63.2 to T+32.8 sec is best fit by a simple power-law model. The power law index of the time-averaged spectrum is 2.05 +- 0.42. The fluence in the 15-150 keV band is 3.8 +- 1.0 x 10^-07 erg/cm2. The 1-sec peak photon flux measured from T+8.25 sec in the 15-150 keV band is 0.0 +- 0.1 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/213486/BA/