Basically yes however it depends on what you are being sued for and if your parents have an involvement i.e. they condoned the behavior, knew about it, encouraged it etc.
Here are some samples:
Can Alex’s parents be held responsible for their son’s actions, even if they weren’t the ones who put the drug in the drink?
It depends. For parents to be held responsible for the harmful acts of their children, they must themselves have committed a fault in the care, supervision, or education of those children. If, for example, Alex’s parents always tolerated his drug habit, this could be considered a failure on their part in their duty to raise their son. They might have to compensate the injuries to William, Thanh Mai, and the neighbours!
In order to avoid being held responsible for their children’s harmful acts, parents must demonstrate that they did not commit any fault in caring for or supervising their children. For example, Alex’s parents could argue that they weren’t even at home and that Alex is old enough to take care of himself. They must also show that they did not commit any fault in bringing up or educating their children. For example, Alex’s parents could prove that they had always raised him well and taught him respect, prudence, safety, etc.
http://www.jeunepourjeunes.com/en/rights_obligations/civil_law/other/344/#
If the answer is in the affirmative he will apparently be tried in the juvenile justice system and will not be tried as an adult. As of today it was not known
whether or not his parents would be held responsible for monetary damages that were caused by the fires. As of today these particular fires have been contained completely.
http://www.nupex.org/blog/
Under Parental Responsibility laws, parents and legal guardians could be liable in a civil suit for monetary damages brought against them by anyone who suffers personal injury or property loss through the actions of an intoxicated person whose intoxication is the result of that parent furnishing the alcohol or permitting the alcohol use.
http://www.lz95.org/lzhs/sap/parents/laws.html
Last month in San Antonio, an assistant principal at Clark High School in the Northside Independent School District filed a civil lawsuit against two students at the school and their parents, seeking monetary damages. The two students had created a web page on MySpace that purported to belong to the plaintiff, Assistant Principal Anna Draker, using her name and picture from the school’s Web site.
If the plaintiff sues and collects substantial punitive damages from both sets of parents, and if the result gets national attention in the press, it might go a long way toward making parents takeresponsibility for the behavior of the underage household members that they are in charge of.
http://frontpage.americandaughter.com/?p=867
It could be the Barker family, not the families of the “Jena Six,” who receive the money from Jena Six Defense Fund.
Pineville attorney Henry Lemoine Jr., representing Justin Barker and his family, said the fund could be used as restitution should the Barkers win their civil suit against the Jena Six and their families
http://www.thetowntalk.com/apps/pbcs.dll/article?AID=/99999999/NEWS/399990136
Filing a Civil Lawsuit
http://www.helpandhealing.org/Civil%20Suit.htm
How do I file a civil lawsuit?
http://www.crimevictimlaw.com/faqs/faqs.html
http://www.querycat.com/faq/619e6ab60255ef697d3c93a12d2999fd
Parents’ Guide Book
http://www.darebox.com/parent_guide.html