If the dependent is a child under the age of 19 or a full time student under the age of 24 and has income from wages reported on a W-2 and the income reported is under $6,300, they do not have to file a federal tax return.
They can file if under the $6,300 amount to get a refund of the federal taxes withheld. If they do file for either the refund or if the wages were greater then $6,300, make sure that they indicate on their tax returns that they can be claimed as a dependent on someone else's return. Also, note that if the income was from self employment, reported on a form 1099-MISC or cash, and the amount is $400 or more they are required to file a return for the income received.
Your state may have other reporting requirements for a dependents income and may be less then the federal requirements, so check with your state tax department website for more information.
