"сертификат" и аффидавит по сути взаимозаменяемы, поэтому "сертификат" либо опускается, либо заменяет "аффидавит"
“Affidavit” and “certificate” have distinct meanings. When the words affidavit certificate are used together, often separated by a backslash mark, it is usually on a form requiring verification of statements already provided in the form, which only requires that basic information be filled in and the form be signed. In these instances, the terms affidavit and certificate are being used interchangeably. Sometimes there may be a certificate that indicates that an affidavit is part of a larger document or record, but an affidavit does not require a separate certificate to be valid.
The word “affidavit” is derived from a Latin expression “He has declared upon oath.” An affidavit is a sworn statement of facts that is signed by the person making the statement. This person is referred to as the “affiant” or sometimes the “deponent.” The body of an affidavit contains the name of the affiant and lists the facts or statements that are being made under oath. An introduction will indicate that the statement is being made under oath and the county and state in which the affidavit was prepared.
A notary or similar official witnesses the affiant sign the document and then signs and affixes a seal to the affidavit to verify that it has been appropriately witnessed and the date it was signed. Affidavits are primarily used in legal proceedings and can be entered into evidence in court. Knowingly putting false information in an affidavit can subject the affiant to the penalties for perjury.
----------
нотариально заверенное свидетельство подрядчика
http://universal_en_ru.academic.ru/779090/contractor's_...
не нотариальное потому, что может удостоверяться не только нотариусом, но и другими уполномоченными лицами(в зависимости от юрисдикции)
-------------
waiver and release of lien
http://www.multitran.ru/c/m.exe?a=4&MessNum=280960&l1=1&l2=2
----------
WHAT IS A CONTRACTOR’S AFFIDAVIT?
A Contractor’s Affidavit is a sworn statement prepared by the Contractor and served on the Property Owner under the following circumstances: (1) when final payment has become due under the prime contract; (2) upon the Property Owner’s request when a progress payment has become due; or (3) when the Contractor is terminated before the Project is completed. The Contractors’ Mechanics Lien Kit contains a Contractor’s Affidavit which can be used for all three of the above situations.
Contents of a Valid Contractor’s Affidavit: To be valid, the Affidavit should include the following information: (1) that all Lienors who have timely served a Notice to Owner have been paid; (2) if all Lienors have not been paid, then identification of each unpaid Lienor and the amount due, or to become due for labor, materials, and services provided to the Property; and (3) the Contractor’s notarized signature. any question you may have about the Contractor’s Affidavit.
Property Owner’s Right to Pay Others Directly: Upon receipt of the Affidavit, the Property Owner may, after providing the Contractor with at least 10 days written notice, directly pay all unpaid Subcontractors, Materialmen, Laborers, and Professionals the amount due from funds owed to the Contractor. In the event there are insufficient funds remaining to pay all Lienors, then the Contractor is required to pay the difference to the Property Owner before the Property Owner pays any of the unpaid debts. If the Contractor fails to provide the Property Owner with the deficiency, then the Property Owner can, upon 10 days written notice, directly pay any unpaid Lienors on a pro-rata basis.
PRACTICE POINTER
If the overall Project has been completed and you have not yet served a Notice to Owner, but are still within your deadline to do so, the Property Owner must pay your claim directly if the Contractor identified you in the Contractor’s Final Affidavit.
Contractor Penalties: If a Contractor fails to provide a Contractor’s Affidavit under the circumstances identified above, then the Contractor will be deemed in default of its contract and lose its Mechanics Lien rights until corrected. Moreover, if a Contractor fails to serve an Affidavit on the Property Owner within 5 days before filing a Lawsuit, then the Property Owner will have a complete defense to the Lawsuit unless the Contractor can timely and properly correct the failure within the statute of limitations period. Further, if a Contractor provides an incorrect Affidavit or fails to list unpaid Lienors who have served a Notice to Owner, then the Contractor may lose it own Mechanics Lien rights.
Property Owner Penalties: The Property Owner is required to retain the final payment until the Contractor has served the Affidavit. If the Property Owner fails to do so, then the Property is subject to foreclosure by any Lienor who has timely and properly recorded and served all Mechanics Lien Documents.


--------------------------------------------------
Note added at 2 hrs (2014-06-25 10:10:24 GMT)
--------------------------------------------------

можно использовать и
"свидетельство под присягой"