There is renewed interest in Mars exploration particularly pertaining to the presence of water and it's implication for life. A model for the martian subsurface constructed by meteorite impacts, volcanism, and fluvial deposition suggests that liquid water could exist below a permanently frozen layer called the cryosphere. The resistivity of the liquid water layer would be much less than the dry surrounding layers creating a geoelectric profile seemingly ideal for magnetotelluric (MT) exploration. A highly anomalous magnetic field would probably not generate electromagnetic plane waves. Therefore, controlled source MT must be used to create the incident electromagnetic plane waves needed for the MT method. The quasistatic approximation required for MT only holds beyond -900 m depth for the model tested. Higher frequency for sensing depths less than 900 m would violate the quasistatic approximation. Computer simulation show that liquid water would be very detectable. Small changes in cryosphere thickness would not be detectable. Changes in salinity of the liquid water give the same apparent resistivity sounding as changes in thickness. No direct conclusions could be drawn about the thickness of the liquid water layer. The data could only provide a maximum thickness estimate.