KM-32P mask is a variation of the basic KM-32 design which allowed pilots to drink water without taking the mask off. Letter "P" in the name of the mask most probably stands for "Pit'evaya" which could be loosly translated in English as "allows to drink".

On outside, KM-32P has a small hole, covered by a rubber plug, on the front nose area of the mask's rubber shell. Inside, a rolled up rubber tube is attached to the opening. It's a simple mechanism that allows to maintain pressure inside of the mask when plug is in place. When plug is removed, pilot can drink the water, though I'm not sure if this lowers the pressure inside of the mask or not.

KM-32P masks were issued in two colors - green and black. It appears that green masks are of early production - upto early to mid 1970s, while masks made after that were all of black color.

 

Fron view of the KM-32P mask. Note the plug which covers the opening through which pilot can drink water.
Plus is removed to show the opening.
On the inside, KM-32P has a rolled up rubber tube connected to the opening in the mask's shell.
Mask's serial is stamped on the band.
Just like regualar KM-32, KM-32P can be equipped with an internal microphone - though most of the masks do not come with it. Note the ID stamp located on the bump - it says that it's a KM-32P mask, size 2 and was produced in 1972. Letter "P" in the name is not stamped out like the rest of the information which suggests that all KM-32 masks came from one assmebly line, then some of the masks were modified to the needed version and stamped with a proper version name.
Shown here is a late production model of KM-32P mask made out of black colored rubber.
Black KM-32P's ID tag. Note that once again, letter is stamped out differently then the rest of the information on the ID tag.
Inside, some of the late production KM-32P masks have a metal mesh that covers inside part of the pressure valve. Possibly this was done to protect the valve from outside objects, but I'm not sure.
Following images show possible pilot setups. First KM-32P is mated with leather helmet as it would have been worn by bomber pilots. Then, KM-32P is displayed as part of the ZSh-3 setup worn by fighter pilots.