GRB 140408***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 (NASA/UMBC), C. B. Markwardt (GSFC), D. M. Palmer (LANL), T. Sakamoto (AGU), M. Stamatikos (OSU), J. Tueller (GSFC), T. N. Ukwatta (MSU) (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 140408***A*** (trigger #595162) (NAME, et al., GCN Circ. xxxx). The BAT ground-calculated position is RA, Dec = 113.596, -50.404 deg which is RA(J2000) = 07h 34m 23.1s Dec(J2000) = -50d 24' 14.7" with an uncertainty of 4.3 arcmin, (radius, sys+stat, 90% containment). The partial coding was 40%. [Description about the mask-weighted light curve] T90 (15-350 keV) is 840.00 +- 0.00 sec (estimated error including systematics). The time-averaged spectrum from TTBD to TTBD sec is best fit by a simple power-law model. The power law index of the time-averaged spectrum is 2.73 +- 0.57. The fluence in the 15-150 keV band is 1.4 +- 0.4 x 10^-06 erg/cm2. The 1-sec peak photon flux measured from T+0.00 sec in the 15-150 keV band is 0.0 +- 0.0 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/595162/BA/