An emergency was issued in Ellicott City in Howard County at 4:40 p.m.
Mr. Miller said Sunday's rain started around 2:45 p.m. and had not yet subsided as of around 6:30 p.m.
Videos and photos posted to social media and shared with Fox 5 showed the city's Main Street - the same street devastated by flash flooding in July 2016 - inundated with severe floods as water rushed through the area.
Howard County Fire and EMS compared the situation to a flash flood in 2016 that left two people dead and forced Ellicott City to rebuild.
"If you are trapped, we are coming", the Howard County Department of Fire and Rescue Services tweeted at one point.
Multiple rescues are under way.
This time, witnesses say, the flash flooding came with a roar of onrushing water after hours of heavy rain had soaked the region around Baltimore.
The Roger Carter Community Center is open for those who need a place to shelter. Portalli's Italian Restaurant employee Arianna Wilgar said the water had reached the establishment's second floor.
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"It took everything I had to get through the last one", she said.
Howard County Executive Allan Kittleman said Monday morning that his priorities are finding the missing man and assessing the condition of buildings that house shops, restaurants and families.
Just two weeks ago, Hogan announced that the Federal Emergency Management Agency had awarded the state and county more than $1 million to pay for projects aimed at reducing the flood risk in areas around Main Street.
Authorities say Ellicott City, on the west bank of Maryland's Patapsco River, is prone to periodic flooding. In addition to the flooding in Ellicott City, flooding was also reported elsewhere in Howard County and in neighboring Baltimore City and county. "You're much safer indoors". The agency added that water had risen above the first floor of buildings in some areas and that it had received reports of building collapses. Cars are getting stuck in high water and basements are flooding, she said, though no injuries have been reported so far.
"We will be there for them as we were in 2016", Kittleman said.
Mike Muccilli, a meteorologist with the National Weather Service in Sterling, Virginia, said it's too early to make comparisons between the two floods.
The National Weather Service called the flooding an "extremely unsafe and potentially catastrophic situation" as the rains pounded the city Sunday evening.
Maryland Gov. Larry Hogan has declared a state of emergency in a community west of Baltimore hit by flash floods. On Twitter, Hogan urged residents to seek higher ground if their area is under a flash flood warning.