What is the correlation between the nth and (n-1)th carry bit being equal and unequal and overflow occuring in the 1's or 2's complement sum

Question

I recently found a problem in which the reason for overflow was that the carry bits were unequal. Is that a valid reasoning for overflow in binary arithmetic ?

I saw that some other reasons for overflow were adding two negatives and getting a positive or changing the magnitude of the value when trying to compress a number into the given number of bits.