Hi and welcome to Just Answer!If your father added your name to his account - that doesn't mean you became an owner of funds - thus is the money are still considered as owned by your father - there is nothing changed.If the money are moved to your account - the question would be - if that is a gift from your father to you? or you just hold funds that actually owned by your father?If the ownership or fund is not changed – there is nothing to worry.If funds are gifted to you - See IRS publication page 34 - http://www.irs.gov/pub/irs-pdf/p525.pdf - Generally, property you receive as a gift, bequest, or inheritance is not included in your income. There is no limit on the value you may receive.You will not owe any federal or state income taxes on that gift - only tax liability would be based on the interest credited on the account.
However the donor (the person who makes a gift) may be required to file a gift tax return if the value of the gift is above $13,000 per person per year. There will not be any gift taxes unless the lifetime limit of $5,000,000 is reached.Let me know if you need any help.