Exhibit 3.2

STATEMENT OF RESOLUTIONS

DELETING SERIES OF SHARES DESIGNATED

SERIES A JUNIOR PARTICIPATING PREFERRED STOCK

OF ATWOOD OCEANICS, INC.

Pursuant to the provisions of Section 21.156 of the Texas Business Organizations Code, the undersigned submits the following statement for the purpose of deleting a series of shares of its preferred stock, without par value, designated “Series A Junior Participating Preferred Stock”:

1. The name of the entity is Atwood Oceanics, Inc. (the “Company”).

2. Pursuant to authority conferred upon the Board of Directors of the Company by the Amended and Restated Certificate of Incorporation of the Company filed with the Secretary of State of the State of Texas on February 10, 2006, as amended, the Board of Directors of the Company duly adopted the following resolutions on December 7, 2012, which resolutions relate to the previously issued dividend of one right (each, a “Right” and collectively, the “Rights”) in respect of each share of common stock, par value $1.00 per share, of the Company to purchase shares of Series A Junior Participating Preferred Stock of the Company (“Series A Preferred Stock”) pursuant to a Rights Agreement, effective October 18, 2002 (the “Rights Agreement”), between the Company and Continental Stock Transfer & Trust Company, as rights agent, each such Right representing the right to purchase one thousandth of a share of Series A Preferred Stock upon the terms and subject to the conditions set forth in the Rights Agreement:

WHEREAS, effective as of the close of business on November 5, 2012, the Rights Agreement (the “Right Agreement”) dated effective October 18, 2002 between the Company and Continental Stock Transfer & Trust Company, as rights agent, expired in accordance with its terms;

WHEREAS, none of the authorized shares of the Company’s Series A Junior Participating Preferred Stock (“Series A Preferred Stock”), which shares were issuable upon the exercise of the rights of the Company’s shareholders to purchase shares of Series A Preferred Stock upon the terms and subject to the conditions set forth in the Rights Agreement, have been issued or are outstanding;

WHEREAS, the Board has determined that it would be desirable and in the best interests of the Company and its shareholders to eliminate the Series A Junior Participating by filing a Statement of Resolutions, substantially in the form attached hereto as Exhibit B (the “Statement of Resolutions”), with the Secretary of State.

NOW, THEREFORE, BE IT RESOLVED, that the terms and provisions of the Statement of Resolutions are hereby acknowledged, approved and adopted in all respects; and further

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RESOLVED, that the Authorized Officers be and each of them hereby is authorized and empowered, for and on behalf of the Company, to execute and file with the Secretary of State the Statement of Resolutions, in order to effect the elimination of the Series A Preferred Stock and the deletion from the Amended and Restated Certificate of Formation of all matters set forth therein with respect to the Series A Preferred Stock and any references therein to the Series A Preferred Stock.

3. The above resolution were adopted by all necessary action on the part of the Company.

IN WITNESS WHEREOF, the Company has caused this statement to be executed on its behalf by the undersigned authorized person this 12th day of December, 2012.

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