It should be written into either your Part 145 MOE or your procedures. If it is, it may well specify what ATA chapters and to what depth (e.g chapter 25 without use of any specialist test equipment).
You also need some means of ensuring the CMM is being kept up to date - no easy matter with so many vendors.
In a nutshell, yes you can so long as you Quality dept have written up what you can and can't do. The NAA has to approve MOE amendments so by informing them of the amendment and assuming they do not knock it back, they (the NAA) are approving your organisation to use the CMM "on aircraft".