After they watched the video and Stefano said Kate saved his life that night she responded with "and killed a man" Kate then said that Stefano covered it up.
In going with that I have to assume the hand that reached for the lamp was Kate’s and she’s the one that hit the Senator over the head and killed him. I’m also going to suspect that they never saw the tape as Maddie got it before they could so they weren’t sure if they were on the tape or not. So, if it got out that was how the Senator died and Kate and Stefano’s voice is on the tape and Maddie was on the floor next to the bed then Kate and stefano would be suspect for sure.