In general, JTAPI provides cause/reason codes associated with object events, e.g.
However, these can bit a bit limited as an infinite number of things that can happen to a call in the CUCM universe must be mapped to a limited number of defined cause/reason codes.
It the JTAPI cause/reason codes are not enough to determine what 'really' happened, you will likely need to have someone look at the detailed CTI Manager and/or Callmanager logs to suss out the specific details...