Montgomery County, Md., police say the man fired at least one shot Tuesday morning at the woman as she left for work. The woman was not hit and fled to a nearby apartment in Bethesda.
The gunman has been identified as 32-year-old Joshua Prince, reports CBS station WUSA in Washington.
While police searched the area in the next few hours, ramps to and from nearby Interstate 270 were closed and exterior doors at two local schools were locked as a precaution.
Police say when they learned that the man was traveling to Pennsylvania, they began to negotiate his surrender and he turned himself in to police there on Tuesday afternoon.