Short answer? Yes.
I love the name "Insane Jane" and the "psychotic smile" as part of the opening. The first sentence is one of the most important, and does a good job catching my interest.
As far as the rest of it goes, it's a solid start. When it comes to mystery stories, I enjoy psychological ones, strategic ones, etc. Something that isn't straightforward and reveals itself slowly. Lots of surprises. Just like chess. One move at a time, each side takes a turn. Making it feel like a fair exchange on both sides, and not just a one-sided solution on the reader's part. If you continue off of what you've already written, I would be happy to read it when it's done.
Other notes: There's a few grammar issues, particularly in how a few extras commas would improve how some of the longer lines read. For example: "Insane Jane flashes her psychotic smile one last time before the FBI agent rolls her straight jacket into the S.W.A.T. van." Even a small change like this can making something easier on the eye: "Insane Jane flashes her psychotic smile one last time, before the FBI agent rolls her straight jacket into the S.W.A.T. van."
