Got Murder? - S3-E12
Continuity mistake: When Catherine is looking through the contents of the birds nest, she takes out the teething ring and places it on a pile on the left. When Gil comes in and asks her what she has, the shot shows the nest and the teething ring is back in it.
Answer: He doesn't have the authority to arrest him - when anyone is arrested in the show, a police officer does it. Also he tells Ty that he is going to be submitting his case findings to Ty's insurance company, who would no doubt contact the IRS, who then would have him arrested for fraud etc.