Yes,, he is demonstrably 'of sound mind''. Because he knew right from wrong and how do we know this? Because he hid what he did, he lied about what he did , he organized his family to lie about what he did , because he didn't want to be caught.
If he was of 'unsound mind' he would have murdered Tia in front of the police station and then knocked on the door for some attention and assistance in his 'event' .
But he didn't. He got her alone and did God knows what before strangled her, stripping her of her clothing , then driving to thriver bank and attempting to throw her body in the Pimpano River. Which is what people who know damn well what consequences are, and what's right and what's wrong , do. .....