Thermal expansion and contraction can cause pipes, ductwork and even floorboards to creak and groan. So can slight flexing of the structure due to wind. Sometimes it can sound like dripping water. Or it might be dripping water in a hidden location. First, you'd need to pinpoint the source of the sound more precisely.

My neighbor had the same problem and discovered bats hanging from the rafters and pooping on the ceiling.

No,it didn't bother him at all. He sent his wife and 2 boys up there to bag the poop up and sold it to organic gardeners.

such a delightful gentleman that neighbor was! lol we used to have that. it was our bumpout or alcove roof, just the right wind and rain would cause it to run in along the eves then it ran down a beam and when there was enough it would puddle in the center of the ceiling. it took almost as long to find and repair multiple times as it took to find it. like a 5 year project it was. everytime we thought we fixed it we had not.

"it took almost as long to find and repair multiple times as it took to find it."

Oh those days before one could turn to the interweb with such perplexing things. Today,we only need to describe the situation in detail as op did here and presto,mystery solved.

oh did that, no one suspected the side of the roof.

The secret to getting help is giving complete details. For a nice example of laying out details,go to the original post in this thread. Using this as a guide,it's possible to find or fix almost anything.

i am not sure what you are trying to say klem. but, in case i was not clear enough, in my case it would go in and run along beams unseen and not showing any wet until it surface at least 6 feet away. yours may not hit totally the right spot or it may take a longer time to show. my mother had a similar situation, but hers was the flashing. hers went on for a few years before her garage ceiling caved in. in the meantime several professionals had claimed they had no clue. hopefully that was clear enough. at least to me the sound like the same problem, potentially. I was checking flashing to chimneys etc. first. to be sure use one of the good goopy things on them so they will stop any potential leakage. I have not met a single professional willing to do this fix,they always want to start over. go in attic during day and carefully look for the sky. smell all walls for mildew. floor for soft spots. anything unusual. as i said it may take a while.

When is the dripping sound most common? After it rains, when a bathroom sink/toilet/shower has been in use? After the AC has ran? Is there a particular area in the home where the sound is more prevalent? If you hire a plumber, ask if they use a thermal imaging camera to search for any leaks.

Have you had your roof, flashing, gutters, or vent pipe checked for any damage or leaks? When was the last time your gutters were cleaned out? Do you have any tree branches too close to the roof? Have you noticed squirrels on your roof? Because squirrels will chew off shingles and make holes. Was your roof checked for damage after a hail storm?

A home inspector can usually help with those types of issues, if you arent comfortable getting up in the attic, or would like a 3rd party opinion.

Couchgolfer, it happens after the ac has run, what shall I do?

Do you have a furnace or a/c unit in the attic ? If so it's probably a clogged condensate line and just needs a regular maintenance visit from a qualified HVAC technician.