You will be asked questions about the backup timing, location, the property at risk, etc.
City personnel will check for blockages in the main line. If a blockage is found, it will be immediately cleared.
If the main line is not blocked, you will be advised to call a plumbing or sewer contractor to check your service line. Maintenance and repair of the service line is the owner's responsibility from the house to, and including, the connection to the city's main sewer. The main sewer is owned and maintained by the City of Liberty.
To minimize damage and negative health effects, you should arrange for cleanup of the property as soon as possible. There are qualified businesses that specialize in this type of cleanup if you'd prefer to not handle the cleanup yourself.