The input common mode voltage is something you can measure
(or assert). (VIN+ + VIN-)/2. It is what it is, depending on signal
sources.
Common mode input -range- is another matter. There will be
different ranges for damage, functional, pristine analog
operation. A product would spec the last, as product electrical
performance table conditions. To find it you would characterize
every "care-about" across an over-the-top common mode input
range and see where things start to fall apart - then back off by
some "feels right" margin for luck in production.
CMRR for a comparator, I would not use but you can measure by
using a classic op amp test loop and let the comparator "chatter
to itself" (OK for clean input, not so trustworthy for a hysteretic
comparator which may have AC aspects which bend "DC" (as
chatter PWM) Vout. Your CMRR (as an amplifier) is
db20(dVout/dVcm) from wherever you call your "0" reference.
Me, I'd be more interested in the front end error, dVio/dVcm
as the linear CMRR also has to do with the highly variable AVOL,
yet most comparator applications care about Vio and tPD with
AVOL being "lost in the bang-bang".