The municipal-bond market has been handed a bullish gift. Now they just have to figure out what to do with it.

The Federal Reserve signaled last week it wouldn’t raise interest rates in 2019, triggering a rally in state and local debt because interest rates and bond prices move in opposite directions. At the same time, record-breaking amounts of cash are coming in: municipal-bond mutual funds have attracted more money in 2019 than they have during the same period of...