You generally should send a thank you note to anyone who gave a gift or helped you during the funeral, but this is not necessarily everyone who signed the Memorial Book. When it comes to family, it is usually not necessary to send thank you notes unless the family member did something beyond what would be expected.
However, when in doubt, use your best judgment as to who you send a thank you to (as all families are different and some will expect a thank you.)
For additional tips, see our guidelines about who should get thank you notes here: