A light curve of the eclipsing binary CM Draconis has been analyzed for the presence of transits of planets of size >=2.5 Earth radii (RE), with periods of 60 days or less, and in coplanar orbits around the binary system. About 400 million model light curves, representing transits from planets with periods ranging from 7 to 60 days, have been matched/correlated against these data. This process we call the ``transit detection algorithm'' or TDA. The resulting ``transit statistics'' for each planet candidate allow the quantification of detection probabilities, and of false-alarm rates. Our current light curve of CM Dra has a coverage of 1014 hr with 26,043 individual points, at a photometric precision between 0.2% and 0.7%. Planets significantly larger than 3RE would constitute a ``supranoise'' detection, and for periods of 60 days or less, they would have been detected with a probability greater than 90%. ``Subnoise'' detections of smaller planets are more constrained. For example, 2.5RE planets with 10 day periods or less would have been detected with an 80% probability. The necessity for predicted observations is illustrated with the nine top planet candidates that emerged from our TDA analysis. They are the planet candidates with the highest transit statistics from the 1994-1998 observing seasons, and for them transits for the 1999 observing season were predicted. Of the seven candidates that were then observationally tested in 1999, all were ruled out except one, which needs further observational confirmation. We conclude that the photometric transit method is a viable way to search for relatively small, inner extrasolar planets with moderate-sized telescopes using CCD photometry with a matching-filter analysis.