Not sure where this originally came from, but I had previously saved this write up.
Looks like you are in good shape with that designation:
General installation of wiring, including installation inside of walls, is governed by 725.61(E), the principal features of which are:
* (1) CL2 and CL3 are always permitted;
* (2) CL2X ("X" is a residential suffix, signifying a lower grade than plain CL2) or CL3X may be installed in raceways;
* (3) CL2X or CL3X, if under 1/4 inch in diameter, may be installed in a 1 or 2 family residential dwelling without a raceway; if non-concealed, it may also be installed in multifamily dwellings.
So, if a cable isn't marked CL2 or CL3, is it suitable for in-wall installation? It may be. The NEC allows cable of a higher rating to be substituted for a lower rating, and therefore, any of the following may be used: CM, CMP, CMR, CMG, CL2R, CL3R, CL2P, CL3P, PLTC. CMX also may be used where CL2X or CL3X is required.