When deducing the return type of sum, we need to deduce the type of all return statements and make sure they are the same.

§[dcl.spec.auto]¶8:

If a function with a declared return type that contains a placeholder type has multiple non-discarded return statements, the return type is deduced for each such return statement. If the type deduced is not the same in each deduction, the program is ill-formed.

For return i , we deduce int, but what do we deduce from return sum(i-1)+i? Can we use the type of sum to deduce the type of sum? Actually, we don't have to. §[dcl.spec.auto]¶11:

If a variable or function with an undeduced placeholder type is named by an expression (§[basic.def.odr]), the program is ill-formed. Once a non-discarded return statement has been seen in a function, however, the return type deduced from that statement can be used in the rest of the function, including in other return statements.

There's also an example which is almost identical to this question (§[dcl.spec.auto]¶general-example-4).

So we can first deduce int from return i, and then use that for the rest of the function.

Note that if we were to invert the if statement and swap the order of the return statements like so, we'd get a compilation error, since we haven't deduced int from return i yet when we encounter the recursive call:

if (i > 1)
  return sum(i-1)+i;
else
  return i;