DoninGA's answer is correct for TurboTax Online users (which is, indeed, the large majority of TurboTax users), but on the off chance you are a TurboTax desktop user, please do the following:
1. I assume that you want to delete the New Hampshire return in its entirety. If so, go to FILE in the upper left, click on it, and scroll down to Remove State Return. If you choose New Hampshire, this will remove not only any data you entered for New Hampshire but also any forms associated with NH included the DP-10. And if you want to remove only the DP-10 and not anything else (like other forms for NH), go to Forms (upper right) and on the left scroll down to NH DP-10. When you click on it to display it, then note the Delete button at the bottom of the form.
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