The CMP has the fastest reload time of any SMG (very nearly the same speed as a pistol), a high fire rate, and good total ammo. The downside to the high fire rate, though, is the unpredictable recoil it shares with the Mark 10. It will often recoil to the sides and downwards. This can make it difficult to use for someone who's not used to this unpredictability.
All these things, combined with the slightly obstructive iron sight, make the CMP strictly a close-range weapon. With certain attachments, you can reduce the recoil to allow it to perform better at medium-range situations. A skilled user can absolutely devastate groups of weak enemies when the time is right.
The CMP is based on the TP9-US, the semi-automatic, civlian version of Brügger & Thomet MP9. It can be easily differentiated from the parent weapon by it's lack of a front grip, with an under barrel Picatinny rail in it's place. The sideways folding stock and top rail mount featured on the CMP are also parts native to the MP9.
The stamping on the left side of the weapon confirms that the CMP is an MP9, though the stamping is partially hidden by the rail mount. The side rail is also unusually located to the left of the CMP rather than on the right like the real-life TP9/MP9.
"CMP" is most probably a reference to the CMP-150, a similar weapon found in the Nintendo 64 video game Perfect Dark, which was based on Steyr TMP, the predecessor of MP9 which is subsequently the predecessor of TP9 on which the in-game CMP is based.
In one of the early builds of Payday 2, FBI Shields used a CMP with a folded stock, a mod unobtainable by the player. This specific CMP can be viewed in the launch trailer of Payday 2, seen from 3:32 - 3:35.
Stubby Compensator could not be installed to the CMP before an update, making it the only weapon that could use some but not all of the standard barrel extensions.
The inventory icon of the weapon shows the gun with the extended mag and without the foregrip, which was added in an update.
Prior to said update which gave the CMP a foregrip, the weapon shared its first person idle animation with the Mark 10.
The Assault Light and Tactical Laser mods are placed on the left side of the gun. This is unusual for a gadget item as one is usually posted on the right-hand side rail instead of the CMP's left.