We call a positive integer N a 4-perfect number if the sum of all divisors of N is equal to 4N. In this paper, we give some sufficient conditions such that an odd integer exactly divisible by 3 2 cannot be 4-perfect. Moreover, we refine Euler's structure theorem on odd 4-perfect numbers given by Broughan and Zhou in the case where N is exactly divisible by 3 2 .