Public visitation was held Wednesday at Carmel Church in Needville.
The funeral is for Rule's family and law enforcement only.
Last Friday, Rule and sheriff's deputies were responding to a call for a property check at a home in the 3900 block of Chestnut Bend.
According to officials, a neighbor called and reported she thought she saw someone running.
Fort Bend County Sheriff Troy Nehls said when deputies arrived at the scene, they entered the home through an unsecured back door.
As they were going through the process of clearing the home, a sheriff's deputy thought there was a suspect inside the house and fired his weapon, killing Rule.
WATCH: Fort Bend County Sheriff Troy Nehls and Pct. 4 Constable Trever Nehls provide update on shooting death of deputy constable
Fort Bend County authorities speak about fallen deputy constable's accidental shooting death
Rule, who was wearing a bulletproof vest, was shot in the chest and flown to Memorial Hermann Hospital, where he died.
Officials are calling this an accidental shooting.
Rule worked for Precinct 4 for nine months. Prior to that, he was a detective for 14 years with the Missouri City Police Department.
Rule has a wife and and four children, including a daughter who graduated from high school the same day he was killed.
The deputy who shot him was placed on administrative leave, which is protocol during officer-involved shooting investigations.
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The video above is from a previous report.