D.C. Mun. Regs. tit. 9, r. 9-208
There shall be credited against and applied in reduction of the tax imposed by § 1 and § 5 of Article 2 of the Act, the amount of any inheritance tax imposed by the District.
Before any credit may be allowed against the tax imposed by § 1 and § 5 of Article 2 of the Act for estate, inheritance, legacy, or succession taxes lawfully imposed by any state or territory of the United States, the following shall be submitted to the Deputy Chief Financial Officer:
If a refund has been made, the date the refund was made, the amount of the refund, and a description of the property or interest with respect to which the refund was made must be shown in the certificate filed under § 208.2(b).
The evidence described in §§ 208.2 and 208.3 should be filed with the copy of the return; Provided, that if the filing is not convenient or possible, it should be submitted to the Deputy Chief Financial Officer promptly after the filing of the copy of the return.
The Deputy Chief Financial Officer may require the submission of additional proof deemed necessary to establish the right to the credit or the final determination of the amount of the State or territorial taxes.
If, subsequent to the allowance of the credit by the Deputy Chief Financial Officer, a refund is made of any estate, inheritance, legacy, or succession taxes paid to a State or territory; the executor or administrator, as the case may be (or, if the refund is made after the executor's or administrator's discharge, then any person or persons to whom the refund is made) shall advise the Deputy Chief Financial Officer of the date of the refund and the amount of the refund, and shall furnish the Deputy Chief Financial Officer with a description of the property or interest with respect to which the refund is made, and pay the tax due as the result of the refund, together with interest on the amount of tax due.
D.C. Mun. Regs. tit. 9, r. 9-208