A minor child claimed on another person's return can claim a standard deduction of $3,605.
Unearned income (such as interest and dividends) over $3,605 is taxable to Kansas, and a return must be filed. If their taxable income is zero, a return is not required.
However, you must file a Kansas Individual Income Tax return to receive any refund of taxes withheld, regardless of the amount of total income.