Even though the official Atlantic hurricane season started on June 1, and we have already had one named storm (Ana), June is usually not a time for a lot of hurricane development. Most storms that do occur form over the Caribbean and the Gulf of Mexico, although as we saw in May, we get the odd storm that transitions from sub-tropical to tropical over the open ocean as well. This article by Ryan Maue describes some of the factors that keep hurricanes from forming in June.

You can read more about hurricane climatology from the National Hurricane Center here.