Which of the following is the correct opening for a codicil?

The correct choice for the opening of a codicil is "I, [Name], of [Address]." This opening statement is consistent with the formal style used in legal documents, particularly in wills and codicils. It identifies the testator (the person making the will) by name and provides their address, which helps to establish their identity and confirm that they are of sound mind and legal standing when making modifications to their testamentary documents.

The other options do not follow the conventional structure for a codicil. While "This codicil amends my current will" describes the purpose of the document, it does not serve as an appropriate opening. Similarly, "This document replaces my previous will" suggests an outright revocation of the previous will rather than an amendment, which is not the primary function of a codicil. Lastly, "I, [Name], hereby resign my gift" incorrectly implies the renunciation of a gift rather than addressing the amendment of a will. Therefore, the first option not only aligns with legal drafting conventions but also provides a clear introduction that signifies the intent of the testator.