There seems to be some confusion here about an object in free fall, such as a ball thrown once it has left the thrower's hand.
Any practical accelerometer measures relative acceleration which is to say the inertial force experienced by its internal "otolith" relative to its housing.
In free fall, the gravitational force experienced by that sensing mass is identical (in proportion) to that experienced by the housing so the registered acceleration is zero (in all directions). The only acceleration that will be measured, is that due to air resistance to the travel of the object such as a ball - which will of course, be mostly directed opposite to the present direction of travel.