Sometimes it seems to rain forever in Cincinnati. Unlike some places, I don't really think there's a particularly rainy season in Cincinnati as rain comes all year round...including thunderstorms. It seems that early Spring (March and April) and then maybe October and November have a lot of rain. Once it starts getting fairly cold, that rain turns into freezing rain or sleet...or even what they call a "wintery mix." Also, because Cincinnati has a very clay-based soil, a lot of places can easily flood or suffer from standing water if it has been raining heavily for quite some time.
April and May are the worst months for rain in Cincinnati. Some years it rains so much the ground gets soaked and the run off from even a light rain can flood your basement. Other years, it's not quite that bad.