Results from a photometric search for extrasolar planetary transits across the eclipsing binary CM Dra are presented. The TEP (Transits of Extrasolar Planets) network has observed this star since 1994, and a lightcurve with 617 hours of coverage has been obtained. The data give a complete phase coverage of the CM Dra system at each of the 3 years of observations, with a noise of less than 5 mmag. New epoch and period values for CM Dra are derived, and a low flare rate of 0.25 hr(-1) has been confirmed. The absence of periodic variations in eclipse minimum times excludes the presence of very massive planets with periods of less than a few years. The lightcurve was visually scanned for the presence of unusual events which may be indicative of transits of extrasolar planets with 'massive earth' sizes. Six suspicious events were found which are being followed up for future transits, by planets with sizes between 1.5 and 2.5 RE (Earth Radii). However, none of these events has amplitudes compatible with planets larger than 2.5 RE. Coplanar planets larger than 2.5 RE and with orbital periods of less than 60 days can therefore be ruled out with a confidence of about 80%. Planets smaller than 1.5 RE cannot be detected in the data without a sub-noise detection algorithm. A preliminary signal detection analysis shows that there is a 50% detection confidence for 2 RE planets with a period from 10 to 30 days with the current data. This data-set demonstrates that it is possible to detect terrestrial sized planets with ground based photometry, and that strong constraints on the sizes of planets orbiting in the plane of the CM Dra system can be set.