Fill the tank, turn off water supply at the wall and take a note of how high the water is in the tank.
If the water level drops in the tank, then that needs to be addressed first.
If the water level stays in the tank, turn the water supply back on, and see if the fill valve is shutting off consistently.
The water in the tank, should stay below the overflow tube.
If the water keeps overfilling, then the fill valve needs work.
It could need a simple cleaning, or a part, or even replacement.
Can you post a picture here less then 800 x 800 pixels as an attachment of the inside of the tank.