Billy & Kim
Your agent should be able to help you and tell you if the improvements had been permitted through the seller's disclosure reports. But bear in mind that permits are mostly needed if there are alterations on the property and these permits are available in the city hall for a price if they are too new to come out of the dataquick reports.
The first place I would start to verify if an improvement has been permitted is to go to city hall and ask to see the permit jacket for the property address. Having experience with La Mirada as both a Real Estate agent and prior resident, I know that the city keeps good records and are very willing to assist. Many times the seller may not know the history of the home if it is an older home. Many of the homes in La Mirada were built in the late 1950's to early 1960's. La Mirada City Hall is located on La Mirada Boulevard across from Biola University.
Hope this helps!
If I can assist further, please contact me @ 714-396-3283!