Can an event on the critical path have non zero slack time in critical path method?
The critical path is:
"the longest path of planned activities [...] to the end of the project"
In what I would call "purely theoretical" Critical Path Analysis, the length of the project is the length of the critical path. Therefore tasks on the critical path have no slack by definition.
In the real world there may be external dates setting deadlines. Therefore although the critical path might take 15 months, if the deadline is not for 16 months, there would be 1 month of slack to tasks on the critical path. Similarly, if the deadline is in 14 months there is negative slack on the critical path.