As the spot can never close exactly at a option strike price, 2 scenarios arises for ATM. Whether it is on ITM side or OTM side.
If the ATM is closed on OTM Side, its value will be 0 or 0.05.
If the ATM is closed on ITM side, its value will be less than or equal to its Intrinsic value.
Eg: Spot at 38050.
38100 CE will be 0.
38000 CE will be <= 50.
38000 PE will be 0.
38100 PE will be <= 50.
Same can be observed from the recent expiry. Screenshots attached
Note: The Intrinsic value of ITM side ATM need not be equal to its Intrinsic value. Based on the LTP, it will be less than or equal to its Intrinsic value. But for sure the theta value will be ZERO in that all Options.