That would be a nice tribute to the fallen officers. Generally, the flag is flown at half-mast for 30 days. The last officer I recall dying in the line of duty, they parked his cruiser in front of the local police station for a month. Many people left a tribute to him in remembrance.
Fortunately, when an officer is killed in the line of duty, he, or she, is not forgotten. Locally, flags are flown at half mast for a period of 30 days. Depending on the location, it may be strictly within their jurisdiction to anywhere in the state. Memorials for these fallen officers are also put on monuments around the country as well as the Officer Down Memorial Page.