BAYTOWN, Texas- There's a push to name the courthouse annex in Baytown after Assistant Chief Deputy Constable Clint Greenwood. 

Greenwood was shot and killed in the courthouse parking lot on April 3. 

RELATED: Deputy constable fatally shot outside Baytown courthouse

Police said William Kenny murdered Greenwood before taking his own life a day later.

RELATED: Suspect in Deputy Greenwood's murder committed suicide, police say

Kenny had an ongoing grudge against law enforcement. 

The Justice of the Peace for Pct. 3 said naming the annex after Greenwood is the right thing to do as a way to honor his 30 years in law enforcement. 

The idea will have to be approved by the county commissioners.