You can't delete your character. You can retire her though and resurrect her. You'll lose a good bit of her work, but I don't believe you get a clean slate with skills.
You can always just start a new detective if you have serious issues with your current one.
Oh, yeah . . . and I made a fatal mistake in accusation, but I don't like to talk about that, lol. Just goes to show you what happens when you try solving mysteries in the morning. ;)
