Murder Riddles

Mr Rogers, Why?

"Who shot her?!" Mr Rogers yelled as he burst into the hospital room.
Before him, his life lay dead, with a bleeding wound, from a bullet, in her head. He collapsed to the floor, yet the Detective helped him to his feet.
"Sir, I know this is a hard time for you, and we don't want to push any stress or shock on you, but we will have to ask you a few questions," the detective said.
Mr Rogers wiped his eyes, and said," Well alright."
"First of all, although you and the victim have been divorced for the past six months, yet you still live in a house together? This is most peculiar," the detective said.
"That is correct, detective."
"Have you been having any trouble recently?"
"Yes, actually. You see, I had to go to a business trip to Cardiff, and my ex-wife was so outraged and upset, she threatened to commit suicide. In fact, I had to yank the bleach bottle out of her hand! But, she calmed down, I don't know why, maybe shock or she had realized how stupid her actions must have been, that she let me go to Cardiff. I had just arrived, when my maid called me, telling me that Josephine had been sent to St Katherine's hospital, and soon after that I rushed home."
"Now, what exactly did your maid say to you when she called you?" The detective asked, finished his notes on the last story.
"Well, let me think. She said, Sir, Josephine has been rushed to St Anne's hospital! She has been mortally wounded. Please come back!" The man said, scratching his chin.
"Thank you, Mr Rogers. We will come back to you," the detective said.
He exited the hospital room, walked over to his colleagues, and said, "I think you should detain Mr Rogers. If he didn't shoot her himself, I am confident he knows who did."

How did the detective know that Mr Rogers did it? If you know, comment! If you liked it, vote!