  E+A galaxies are characterized as a galaxy with strong Balmer absorption
lines but without any [OII] or Halpha emission lines. Strong Balmer absorption
lines indicate that E+A galaxies have experienced a starburst within the last
<1-1.5 Gyr. However, the lack of emission lines indicates that E+A galaxies do
not have any on-going star formation. Therefore, E+A galaxies are interpreted
as a post-starburst galaxy. However, it has been a mystery why E+A galaxies
underwent a starburst then stopped abruptly.
  One possible explanation to E+A galaxies is the dusty starburst scenario,
where E+A galaxies have on-going star formation, but optical emission lines are
invisible due to the heavy obscuration by dust. To test this dusty starburst
scenario, we have observed 36 E+A galaxies carefully selected from the SDSS DR1
in 20cm radio continuum using the VLA. Since the radio emission is not affected
by the dust extinction, the SFR in dusty galaxies can be revealed by the 20 cm
continuum. All of our 36 target E+A galaxies are selected to have H\delta EW
greater than 6A and no detection of [OII] or Halpha emission lines within 1
sigma. These selection criteria are much stronger than previous E+A selections
in our attempt to select galaxies in the pure post-starburst phase without any
remaining star formation. Except for the two galaxies with a nearby radio
source, none of our 34 E+A galaxies are detected in 20 cm continuum to the
limits reported in Table 1. The obtained upper limits on the radio estimated
SFR suggest that E+A galaxies do not possess strong starburst (> 100 Msun
yr^-1) hidden by dust extinction for the whole sample while 15 (z<0.08) E+As
have lower SFR upper limits of ~15 Msun yr^-1. (Abridged)
