Could it be that Tia died naturally and SH panicked?,i mean with the convictions he has etc,and i reckon he wouldnt be the biggest fan of the police,probably feels theyre always out to pin things on him from past experiences so i doubt hed go to them..
Now the above scenario i reckon would only happen if he walked in on her body,if she had been dead some time,i think if she died naturally in front of him(thinking heart/asthma attack or similar) i think hed panick and call ambulance whilst trying to revive her..
Just a couple of thoughts..