Smith's wife, Kellie Smith, also a BART police officer, told the TV station that she "cherished every moment" she had with her husband, a 23-year BART police veteran who oversaw the department's detective unit.
The couple has a 6-year-old daughter.
Funeral services for Smith have been scheduled for Jan. 29 at a church in Castro Valley, BART Police Chief Kenton Rainey said. The event will be open to the public.
Smith was shot while searching the apartment of John Henry Lee, 20, a suspect in several robberies on BART property.
BART police said in a statement that the San Leandro Police Department had arrested Lee on Jan. 16 after an automobile burglary and subsequent chase that ended when the suspect lost control of his vehicle and hit a tree.
Lee has pleaded not guilty to second-degree robbery with use of a handgun.
Also Thursday, Rainey told the BART board during its regularly scheduled meeting that two BART uniformed officers wore lapel cameras during the search, but he does not know whether the shooting was captured by the cameras.