inquisitory

/ɪnˈkwɪzɪtɔri/
adjective
  1. Tending to ask many questions; curious in a thorough or intrusive way.
    • I tried to avoid my inquisitory neighbor, who always wanted to know my business.
    • His inquisitory nature made him a great journalist but an annoying dinner guest.
    • The child's inquisitory questions about the universe never stopped.