Monette was last seen over a month ago leaving a popular bar in Lakeview.
New Orleans police and a specialized search company from Texas checked areas of Lakeview, Gentilly, and City Park where Monette may have traveled but found no sign of the woman.
State Rep. Austin Badon requested that the state agents get involved.
Wednesdays search included the use of ATVs in wooded areas and a boat on Lake Pontchartrain. Future plans could also include a search plane.
Also Wednesday, Crimestoppers announced the reward in the case had reached $20,000.