I use http://www.greatschools.org to find out. Then I follow up with a call to make sure. Culver can be tricky as it can be different from one side of the street to another. Culver does have a little known secret though. If you look at the color of the street sign it will tell you a lot.
The district has a map onlilne that you can take a look at. The boundaries are kind of uneven, so some areas across the street from eachother are in different districts. Culver City School District will require a permit if you are not in the district to attend Culver City Schools, so if this is your goal, you have to be very careful where you purchase property. The web addy for the district is http://www.ccusd.org