Heavy rains flooded some roads across Connecticut Tuesday as officials urged residents to exercise caution while traveling.

By the end of rush hour Tuesday morning, New Haven had received one month’s worth of rain in one night. That’s according to the city’s Director of Emergency Operations, Rick Fontana. He said the double whammy was that it peaked right at high tide, flooding a dozen roads, the school bus terminal and shutting down a post office.

“I think the worst has passed for right now. But again, you know, we are on a 12-hour cycle for our second high tide day, which will be 8:30 [Tuesday night], and we’re going to be in the same position.”

Fontana said the situation is exacerbated by the city’s old drainage system. New Haven has applied for a $26 Million dollar FEMA grant to dig a new wider one.

Meanwhile, a flood warning is in effect until 4 p.m. Tuesday for parts of northern Connecticut.

Around 10 a.m., heavy rain was filling rivers and tributaries that feed into the Connecticut River as well as the Hockanum River, the National Weather Service said. Up to 3.5 inches had fallen by 10 a.m., officials said.

A flood advisory was in effect for parts of southern Connecticut through midday Tuesday.

Combined with high tides in New Haven at 8:10 a.m. and 8:27 p.m. Tuesday, “there is the possibility that areas of the city and roadways can become flooded without warning and become dangerous and cause damage quickly,” New Haven Mayor Justin Elicker wrote on Facebook.

A flood watch remained in effect through Tuesday afternoon. The flood watch includes parts of northern Connecticut, including Hartford, Tolland and Windham counties.

Up to 2 inches of additional rain was expected to fall Tuesday across southern New England. Some areas may get up to 4 inches. Excessive runoff may result in flooding of rivers, creeks, streams, and other low-lying and flood-prone locations, the National Weather Service said.

Rain-slicked roads caused traffic tie-ups across the state early Tuesday morning. There were no significant issues reported as of midday Tuesday.

Connecticut Public Radio’s Jennifer Ahrens contributed to this report.