Even with all the recent snow melt, flooding on the area rivers at this point is not expected to become an issue. The lack of heavy rain will keep river level well below flood stage through the weekend. One concern that could creep up with the rapid melt would be ice jams which could cause some isolated flooding and fluctuations in river levels.
Here's a look at the Blanchard River in Findlay through the weekend:
Here's a look at the Maumee River in Waterville through the weekend: