I got the answer So I am posting it here :)
The first packet the DHCP Client initiates would be the DHCP Discover packet.
The DHCP Discover packet is broadcast in nature and would be received by both the DHCP servers.
The DHCP servers would respond with DHCP offer packet containing the IP addresses which they offer.
Based on the first DHCP offer the client receives, the client would respond with DHCP request packet which contains the IP address which it would be using along with the DHCP servers IP address which had provide the respective.
This packet is send as broadcast. The packet, when received by the other DHCP server would understand that the IP address which it had leased to the client (In the DHCP offer packet) is not taken. So the DHCP server would put the IP address back to it’s pool.