Your child will need to file a federal income tax return (1040) if their yearly income is over $12,200. In Connecticut, a single person whose gross income is more than $15,000 must file an income tax return.
Even if you child has income under $12,200, most kids will want to file an income tax return, for the experience, and to get their refund. Many summer jobs will withhold income taxes and the only way to get your refund back is to file your tax return.