A case can be made that everyone in the play (with the possible exception of Benvolio) is in some way responsible for the tragic outcome. In the case of the parents, they failed to heal the rift between the two families, causing Romeo and Juliet to hide their love instead of seeking their parents' approval. The Capulets in particular pushed matters to their conclusion by forcing Juliet to accept marriage with someone who they knew she did not want to marry.
Paris
Juliets parents because they wont let them get married.
They are very shocked and sad, of course.
They think that she is depressed over the death of Tybalt
Both of Juliet's parents want her to marry Paris.
Parents teach their children on how to behave.
Parents are fully responsible for their minor childrens health, and that includes their emotional well being as well.
It depends partially on the age of the children. If they are not adults, the parents are responsible. If the children are above the age of majority, and not on their parents' insurance, they should be responsible for their own debts.
Paris
The parents of Juliet believe she died from sadness
Juliets parents because they wont let them get married.
They are very shocked and sad, of course.
After the play, Juliet's relationship with her parents would likely be strained as they were responsible for orchestrating the events that led to her tragic death. They may have felt guilt and sorrow for their actions, causing tension in their relationship.
Parents should be interested in their childrens education so the children don't fail.
It's a general legal principle everywhere that parents are held liable for the actions of their minor children.
They think that she is depressed over the death of Tybalt
They don't say much about it one way or the other.