A ceiling that is uniformly wet or damp with beads of water across a large area may be due to a filter issue with the air conditioner. When an air conditioner runs with a clogged or dirty filter, it will be difficult for the unit to pull in enough air to dehumidify and cool. This leads to the air emanating from the air registers in the home causing more humidity, which can create wet stains around air registers and general humidity issues in the home.
When a ceiling is wet directly under the attic air handler, an issue at the condensation pan may be to blame. If the air conditioner is not regularly serviced or ran for any length of time without a filter, the condensation pan drain can clog with hair and debris. This leads to an overflowing of water over the edge of the pan. New air conditioners have switches that will shut down the unit when overflow occurs, but older models may not; significant damage can occur before the homeowner realizes a problem exists.
Condensation drains away from the air handler in the attic by way of a drain pipe and a condensation pump. The pump pulls the water from the pan and drains it outside or into a floor drain under your house. Any damage or breaks in the condensation drain pipe can cause a leak. Examine the area in the attic directly above the water damaged ceiling for any signs of a damaged condensation pipe and repair or replace as necessary.
Window air conditioners can cause increased indoor humidity and result in water accumulation on the ceiling when their compressors are not running. This can be due to a mechanical malfunction or the temperature being set too high preventing it the from cycling and cooling the air. When the compressor is not running, the unit cannot remove the humidity from the air and instead cycles it back into the home.