Yes, Illinois was #1 in rainfall last month, making us the wettest state in the country:
The National Centers for Environmental Information (formerly NCDC) released their numbers for June, showing that Illinois did indeed have its wettest June on record with 236.2 mm (according to their calculations). That made Illinois the wettest state** in the US for the month.
**There are no statewide records for Hawaii. However, an examination of the four main sites in Hawaii indicate June totals that are far less than 9.3 inches.
Illinois, Indiana, and Ohio all had their wettest months in the 121-year record; Arizona, Pennsylvania, New York, New Jersey, Vermont, Maryland, Virginia, and New Hampshire had top-5 wettest months ever.
The weather patterns causing all this rain, by the way, are related to global warming, and similar to the patterns causing frequent polar vortices in the eastern U.S. Welcome to the future!