According to Section 9-513 of Revised Article 9, the answer depends on the type of collateral covered by the financing statement.
If the collateral is consumer goods, the secured party of record is required to file a termination statement within one month after there is no obligation secured by the collateral and no commitment to make an advance, incur an obligation or give value to the debtor. However, if the debtor sends an authenticated demand to the secured party, the secured party must file the termination statement within 20 days of the receipt of the demand, if the expiration of the 20 day period is earlier than the expiration of the one month time period.
If the collateral is NOT consumer goods, the secured party is not required to file a termination statement unless the secured party receives an authenticated demand from the debtor. If a demand is received, the secured party is to within days 20 days of the receipt, either file a termination statement or send the the termination statement to the debtor.
The proper place to file the termination statement will depend on whether or not your state, New Hampshire, adopted any non-uniform provisions regarding filing of termination statements. The proposed Revised Article 9 text required all Article 9 filings made after the effective date, including terminations of pre-Revised Article 9 financing statements, except those closely related to real estate (as- extracted collateral, fixtures and standing timber) to be filed in a central filing office but the state legislatures were free to adopt other provisions. I suggest you contact a local commercial law attorney to determine whether or not dual releases are required under New Hampshire law.