Galaxies several hundred Myr past a major star formation epoch may show strong signs of the residual starburst population in the form of Balmer emission from A-stars superimposed on an older population, the so-called "E+A" galaxies. Radio emission from such galaxies, absent ongoing star formation, is expected to be minimal. Indeed, Goto (2004, A&A, 427, 125) did not detect E+A galaxies lacking optical signatures of current star formation at 21 cm. Any radio emission from these galaxies is generally assumed to arise from star formation, not AGN, and it is often used to estimate the current star formation rate independently of obscuration. However, the archetypal E+A galaxy G515 (Oegerle et al. 1991, ApJ, 381, L9; Liu et al. 2007, ApJ, 658, 249) has no detectable [OII] or H-alpha emisssion, yet it possesses a core radio source and possibly extended emission. VLA data taken at different epochs show 21 cm continuum fluxes of 3.0 +/- 0.5, <0.5, and 0.65 +/- 0.09 mJy using the D, B, and A array configurations, respectively. The latter two values probably indicate source variability, and hence likely a low-luminosity AGN, though more data are required for confirmation. The higher D-array flux could arise from extended radio emission, presumably from extended and obscured ongoing star formation. Moreover, G515 is not unique. Nearly half, possibly more, of the radio detections in a sample of E+A galaxies with little or no detectable [OII] and H-alpha emission are anomalous, in that they either exhibit extended emission or nuclear point source variability. Variability is confirmed in one of the sources. Hence, low level AGN activity is responsible for the emission in some, possibly a substantial fraction, of E+A galaxies with detectable radio flux. This is an important consideration when using post-starburst galaxy radio emission to measure ongoing obscured star formation.