i created a UPBGE script (which can easily be converted to be used in BGE) which allows the player to grab, drop and throw objects (which are rigid bodies) by pressing the left mouse button to grab and release the left mouse button to release the object. Hope you like it.
P.S. - If you improve the script or do a tutorial on youtube tell me here below!
Grab and release Physics.blend (800.3 KB)