Wilson was found guilty of killing two undercover NYPD detectives during an illegal gun sting on Staten Island.
He received a death sentence in 2007, but an appeals court threw it out.
Now, a jury will decide whether Wilson will be executed or spend the rest of his life in prison.
Wilson, now 31, was a young gang member on Staten Island when he was arrested in the point-blank shootings of undercover officers James Nemorin and Rodney Andrews in an illegal gun sting gone awry. The officers were both shot in the back of the head.
Defense attorneys had sought to head off a second death penalty proceeding by arguing that Wilson's rights were being violated because he's mentally disabled. But a judge found otherwise, citing testing over the years that nearly always found that the defendant had an IQ higher than 70 - considered a benchmark for mental disability.