That's a good question! I'd never thought of it
before. Because most buildings are not built
air-tight, air pressure can equalize inside the
building, so yes, you are generally under the same air pressure inside a building as you are outside.
Pressure works horizontally as well as vertically, and air can be forced into or out of a building through cracks in windows, ventilation systems, open doors and windows, etc.
The difference in air pressure inside and outside a building due to the difference in the weight of the air is probably small compared to the difference in air pressure inside and outside a building due to other effects. As wind blows past a building, it will cause a large difference in air pressure inside versus outside the building, as will differences in air temperature (if the building is heated or cooled, for example) and humidity.
According to the EPA, even an elevator moving inside a building will create air pressure
differences great enough to generate air flow
inside the building. The EPA and other regulatory
agencies, as well as architects and building
contractors, study the flow air through large
buildings for health (ventilation) and comfort
I guess the real question is: If you could somehow make a building completely airtight and never open any doors or windows and never cause any changes in air flow inside the building (no fans, elevators, etc), would you be able to measure a small difference in air pressure
inside the building versus outside the building?