To expand somewhat on HiddenWindshield's answer:
From an ATC perspective we don't know and don't care if an airport is publically (municipally) owned, or privately-owned but public-use, or privately-owned and restricted-use. The regulations for ATC don't take that into consideration. The pilots request to fly into a given airport and ATC provides the relevant and required spacing and sequencing services without investigating further; if it turns out that the pilot didn't have permission to use the airport that's between the pilot and the airport owner, and possibly the local Flight Standards District Office.
As far as airports are concerned, there are two major categories:
All towered airports will reside within some form of controlled-to-the-ground airspace (at least during the hours when the tower is open). This is airspace in which some form of air traffic control is available. In all types of controlled airspace, aircraft operating under Instrument Flight Rules (IFR) are provided separation between each other.1 Whether IFR aircraft are provided some type of airborne separation between them and aircraft operating under Visual Flight Rules (VFR), and whether two VFR aircraft are provided airborne separation between each other, depends on the specific class of controlled airspace.
Some non-towered airports exist in controlled airspace that extends to the ground, in order to provide better service to IFR aircraft operating there, or because they are very close to a towered airport. Many more non-towered airports exist in uncontrolled (Class G) airspace. Generally, all airspace up to at least 700' AGL (in most of the country 1200' AGL, and in certain isolated areas up to 14,500' MSL) is uncontrolled.
So as HiddenWindshield said, at many of those non-towered fields and helipads, there is no ATC service available, not even from Center (because the field exists in low-level uncontrolled airspace). Even at fields within controlled airspace, ATC will only
"clear" a helicopter for landing or takeoff if they are operating on the movement area (ATC-controlled region) of a towered airport. A helicopter operating at an off-airport helipad or even on a non-movement-area ramp at the airport will be told that landing or departure will be "at their own risk," meaning it is up to the pilot to check their surroundings and ensure the safety of the operation.
1Except in Class F airspace, which the US does not have but does exist in other countries.