C/2002 CE$_{10}$ is an object in a retrograde elliptical orbit with Tisserand parameter $-0.853$ indicating a likely origin in the Oort Cloud. It appears to be a rather inactive comet since no coma and only a very weak tail was detected during the past perihelion passage. We present multi-color optical photometry, lightcurve and thermal mid-IR observations of the asteroidal comet. textcolor{blue}{ With the photometric analysis in $BVRI$, the surface color is found to be redder than asteroids, corresponding to cometary nuclei and TNOs/Centaurs. The time-resolved differential photometry supports a rotation period of 8.19$pm$0.05 h. The effective diameter and the geometric albedo are 17.9$pm$0.9 km and 0.03$pm$0.01, respectively, indicating a very dark reflectance of the surface. The dark and redder surface color of C/2002 CE$_{10}$ may be attribute to devolatilized material by surface aging suffered from the irradiation by cosmic rays or from impact by dust particles in the Oort Cloud. Alternatively, C/2002 CE$_{10}$ was formed of very dark refractory material originally like a rocky planetesimal. In both cases, this object lacks ices (on the surface at least). The dynamical and known physical characteristics of C/2002 CE$_{10}$ are best compatible with those of the Damocloids population in the Solar System, that appear to be exhaust cometary nucleus in Halley-type orbits. The study of physical properties of rocky Oort cloud objects may give us a key for the formation of the Oort cloud and the solar system.
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