We analyze two pre-supernova (SN) and three post-SN high-resolution images of the site of the Type II-Plateau supernova SN 2006my in an effort to either detect the progenitor star or to constrain its properties. Following image registration, we find that an isolated stellar object is not detected at the location of SN 2006my in either of the two pre-SN images. In the first, an I-band image obtained with the Wide-Field and Planetary Camera 2 on board the Hubble Space Telescope, the offset between the SN 2006my location and a detected source (Source 1) is too large: > 0.08, which corresponds to a confidence level of non-association of 96% from our most liberal estimates of the transformation and measurement uncertainties. In the second, a similarly obtained V-band image, a source is detected (Source 2) that has overlap with the SN 2006my location but is definitively an extended object. Through artificial star tests carried out on the precise location of SN 2006my in the images, we derive a 3-sigma upper bound on the luminosity of a red supergiant that could have remained undetected in our pre-SN images of log L/L_Sun = 5.10, which translates to an upper bound on such a stars initial mass of 15 M_Sun from the STARS stellar evolutionary models. Although considered unlikely, we can not rule out the possibility that part of the light comprising Source 1, which exhibits a slight extension relative to other point sources in the image, or part of the light contributing to the extended Source 2, may be due to the progenitor of SN 2006my. Only additional, high-resolution observations of the site taken after SN 2006my has faded beyond detection can confirm or reject these possibilities.
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