We know that if the decisional Diffie-Hellmann problem is hard then the Elgamal encryption is CPA-secure. One show that if the chosen group is $\mathbb{Z}_p^*$ then the decisional Diffie-Hellman problem is not hard. For instance, one realizes that $g^{ab}$ is a square with probability $3/4$ with an argument based on the parity of $a,b$. Therefore, it makes self to ask the following question:
Is there a CPA-attack on Elgamal when used with $\mathbb{Z}_p^*$?
I need some help on the way to go here. Should I try to build a distinguisher using the above fact about the Diffie-Hellman problem? Or does is just come from the algebraic structure of the group?