What is the minimum allowed altitude for helicopters over a residential area in the US?
It depends on where it is.
A residential area/houses may or not be &quot;congested&quot; -- that term is not defined. But we typically use 500 feet for helis.
When hovering in an area for a specific purpose, such as photo shoots or other surveillance operation, or for some other operational reason, then we can use a lower altitude.

Sec. 91.119
Minimum safe altitudes: General.
Except when necessary for takeoff or landing, no person may operate an
aircraft below the following altitudes:
(a) Anywhere. An altitude
allowing, if a power unit fails, an emergency landing without undue
hazard to persons or property on the surface.
(b) Over congested
areas. Over any congested area of a city, town, or settlement, or over
any open air assembly of persons, an altitude of 1,000 feet above the
highest obstacle within a horizontal radius of 2,000 feet of the
aircraft.
(c) Over other than congested areas. An altitude of 500 feet
above the surface, except over open water or sparsely populated areas.
In those cases, the aircraft may not be operated closer than 500 feet
to any person, vessel, vehicle, or structure.
(d) Helicopters,
powered parachutes, and weight-shift-control aircraft. If the
operation is conducted without hazard to persons or property on the
surface--
(1) A helicopter may be operated at less than the minimums
prescribed in paragraph (b) or (c) of this section, provided each
person operating the helicopter complies with any routes or altitudes
specifically prescribed for helicopters by the FAA; and
(2) A powered
parachute or weight-shift-control aircraft may be operated at less
than the minimums prescribed in paragraph (c) of this section.]