We had drips from ceiling right below bathtub upstairs. It only happened when the tub was filled with water(even small amount, so probably not overflow issue). I don't see any bathtub crack. What can be the root cause ? Thanks!!
You have not yet established whether the leak is in the supply valves or in the tub or drains.
With the tub valves off for a sufficiently long time, I presume you have no leaking, right? If so, that eliminates the supply piping before the valve seats. When you open the valves, water is admitted into the mixing chamber of the valve and it could be leaking as you fill the tub (crack in the valve body or around the valve stems).
Fill a bucket elsewhere in the house and pour it into the tub. If it leaks, then you have eliminated the valve(s) and it is in the drain of the tub. If it does not leak, it is in the valve(s).
I would plug the tub drain, place a stack of coins in the bathtub, and fill up water to the level of the coins. Wait for some time and if the water level is below the coins, then you have a crack in the tub. Else it's your drainage that is leaking.