Weather Underground has a story describing some of the June tropical storms that were memorable for the amount of rain that was dropped during the storm. You might recognize some of these names, many of which were retired after their spectacular flooding.  June storms are often so wet because they are slow-movers, which allows a longer time for rain to accumulate at any one spot.  A quick rule of thumb is that the amount of rain dropped by a tropical storm is 100 divided by the forward speed.  So if a storm is going 10 mph, then you can expect up to ten inches of rain.  If it is going just 3 mph forward speed, you can expect up to 33 inches. You can read the story here.