This might be Blassreiter. It's mechanical demons, not robots, though.
The story is set in a fictional Germany and centers on the outbreak of biomechanical creatures called "Demoniacs", who rise from corpses and attack people savagely. The Demoniacs have the ability to merge with most technology including cars and motorcycles, not only gaining control of them but also enhancing their performance greatly. Against them is a group of people known as XAT, Xenogenesis Assault Team, who police these Demoniacs in an attempt to keep the peace and discover the reasons for the "Demoniac" change. All the while, a number of human-turned-Demoniacs appear. Some use their powers for good, others for evil. One will rise above all other Demoniacs to become known as the "Blassreiter".
....
Malek, who has been ridiculed and attacked by his school's seniors since he was adopted by Amanda, is distraught by the death of Gerd. He believed that Gerd would punish his attackers, but Gerd ended up being a "coward" by letting himself be killed. When Malek's friend Johann commits suicide after realizing his mistakes in ridiculing, he wonders why no one will stand up for justice. After being offered a pill by Beatrice, Malek transforms into an Amalgam. Malek kills the delinquents and is hunted down by XAT. Joseph, who had met Malek before, attempts to stop Malek from losing control and intervenes, while Brad is shooting thermal shots on the roof top a couple buildings away. Before Brad is about to shoot to start shooting, Joseph jumps in front of Malek to take the shot for him, causing Joseph to be severely injured. Amanda and Al start firing at the wounded Joseph, but Malek shouts and Amanda starts to recognize his voice. Brad shoots at Malek's shield and destroys it, and aims for another shot to Malek's head. Amanda realizes that the Amalgam is actually Malek, and before Brad shoots, Amanda jumps in front of Malek to block it, barely missing her and Malek, who flees, carrying the body of the wounded Joseph. The two escape together while Joseph is unconscious. They go to an abandoned church, where Malek attempts to try and heal Joseph. They are then found by Xargin, who Malek sees as an enemy, and attacks him. Joseph tries to warn Malek not to, but Malek still does, but he gets beaten by Xargin easily, and gets knocked unconscious. Eventually, they are found by Amanda and Hermann. Malek falls into a coma and both are captured by XAT. At the same time, XAT is facing a critical crisis. Their commander, Wolf, has slowly begun to degenerate into a Demoniac. He turns on XAT by infecting everyone, except for Hermann and Amanda. Their comrades die to protect the two from becoming a Demoniac. The two escape via helicopter, but Hermann is forced to crash the helicopter. Using a XAT Paladin, Amanda flees and decides to pursue Joseph.
From TVTropes:
The bullet that Brad carries around his neck is later used to Mercy Kill his old partner, Lena.
However, I have found no evidence that it showed on MTV.
I found it searching for cartoon cop robot partner bullet "around his neck"
