"We are going to close this case," McCarthy said Monday. "There's not a doubt in my mind."
Shortly before 1 p.m. March 11, Jonathan Watkins was sitting with his daughter in a minivan parked in the 6500 block of South Maryland Avenue when a gunman emerged from a gangway and opened fire, police said.
Both were struck and taken to different hospitals. Jonylah was pronounced dead early the next morning after undergoing extensive surgery at Comer Children's Hospital at the University of Chicago.
At his now weekly news conference calling for stricter gun control laws, McCarthy said some of what was initially reported about the Watkins shooting was not true.
"First of all, [Jonathan Watkins] was not changing the baby's diaper when this occurred, and we found no evidence that the mother, his wife, was ever shot," McCarthy said, referring to statements by relatives of Jonylah's mother, who said Judy Watkins was shot while pregnant with Jonylah.
McCarthy said police believe Watkins was sitting in the driver's seat of the van with Jonylah on his lap when the shooter approached from the sidewalk and shot "over his right shoulder."
"The other thing that was significant was the baby was hit with one bullet, not five," McCarthy said.
McCarthy said Jonathan Watkins is talking with police.
"At this point, we think there's a lot more he could help us with, but he is cooperating with the investigation," McCarthy said, crediting the Rev. Corey Brooks for "an amazing job of really trying to get that to happen."
At the news conference, McCarthy continued to call for stricter gun laws in Illinois that he said will help lower crime and reduce the flow of guns onto Chicago's streets. McCarthy said police have seized 1,400 guns so far in 2013.
McCarthy advocated a legal requirement to report the loss, sale or transfer of a gun, something he said will make it easier to clamp down on "straw purchases."
The superintendent also called for a mandatory minimum sentence of three years for serious gun offenses, with a requirement that those convicted serve at least 85 percent of the sentence. The current mandatory minimum for such crimes is a year in jail.