The verb implicate means "to connect or involve in something." For example, your cousins might implicate you in the planning of a big party for your grandparents.
Implicate comes from the Latin word implicare, meaning "to entwine, involve." When you implicate someone, you bring him or her into a group or to pitch in on a project. Implicate can have criminal connotations when it means "to connect in an incriminating manner," like when detectives figure out who drove the getaway car in the bank robbery — that person will be implicated for his or her role in the crime.