Sheriff Tate is aware of the problems that will arise if he decides to charge Boo Radley with murder (albeit in self-defense). Boo will have to make appearances in court, as will Jem and Scout, and the sheriff decides that justice will be best served by calling Bob Ewell's death a self-inflicted accident.
"To my way of thinkin', Mr. Finch, takin' the one man who's done you and this town a great service an' draggin' him with his shy ways into the limelight--to me that's a sin. It's a sin and I'm not about to have it on my head."
As Sheriff Tate says, "let the dead bury the dead." He believes that Ewell got what he deservea by trying to harm Jem and Scout and that Boo was only protecting the children. His decision is best for all involved.