Speaking of a murderer who was apprehended in 1998, a law enforcement officer was quoted as saying:
When all this happened, if I wasn’t there, he may have gotten away with it.
As the speaker was there in the past and the murderer did not get away, standard usage calls for this construction:
When all this happened, if I hadn’t been there, he might have gotten away with it.
Might is the past tense of may. Ideally, may is the form to use when talking about a current situation, and might is the form to use in referring to an event from the past. In practice, the two forms are used interchangeably, as demonstrated by these headlines from different Web sites:
10 Civilizations That Might Have Beaten Columbus To America
Polynesians may have beaten Columbus to South America.
US-bound passengers may have to switch on mobile phones for security
[Cellphone] owners might have to undergo extra screening before boarding
Researchers May Have Discovered The Consciousness On/Off Switch
Scientists might have just found the brain’s “off switch”
6 Signs That You Might Be Psychic
Signs You May be Psychic
7 Mistakes You Might Make Before Your Job Interview
5 Money Mistakes Even Good Savers May Make
Fans might have to wait weeks before Dodgers games come to their TVs
Apple Fans May Have to Wait Longer for Larger iPhone
Most of the time, the interchange of may and might does not present a problem. The Oxford Dictionaries site declares that if the truth of a situation isn’t known at the time of use, then either is acceptable.
The one context in which might is always the better choice is one in which the event mentioned did not in fact occur:
If JFK had not been assassinated, civil rights legislation might have been delayed.
If the English had defeated the Normans at Hastings, we might have inherited fewer spelling problems.