Good morning Shastatrader:
You can only redeposit those funds within the 60-day window if the beneficiary's school returns money previously taken as a qualified withdrawal to you, such as a tuition reimbursement. Otherwise, the plan administrator will treat the replacement money as a new contribution. It would not change the distribution amount shown on your 1099-Q at year-end.
You do have options, and I would refer you to this article. Note that there's no such thing as a trustee-to-trustee "in-state" rollover. The IRS would consider this to be an investment change, even if switching between two different plans in the same state. You would need to roll those assets to an out-of state plan. So if you're thinking of using the recontribution as a rollover, you'll need to open an account with an out-of-state plan (see this article for more information).
VP, Research & Development
This information does not constitute tax advice and is provided for informational purposes only. Please consult your tax advisor, financial advisor, local taxing authority, and/or plan provider or sponsor for more information.