Legally, yes, they should accept a small estate affidavit. Whether or not they actually will is a different question,and a question only they can answer. So ask them before you do anything else.
Also, you should know that a small estate affidavit actually involves probate judge. If you're hoping to have your affidavit approved by the judge, I would at least consult with a probate lawyer. Many probate attorneys offer free consultations and charge very reasonable fees for small estate affidavits. With an attorney, your odds of getting the inheritance smoothly improve dramatically.
DISCLAIMER: Nothing in this answer constitutes legal advice. If you have a legal question, you should consult an attorney. Further, nothing in this answer shall be construed to have started an attorney-client relationship. No such relationship exists until you sign an engagement letter with the Firm. Visit http://www.shuttlawfirm.com or email firstname.lastname@example.org. You may also call Mr. Shutt, a Dallas probate attorney and wills attorney, at (214) 302-8197 for more information on the topic discussed.
I am very sorry. A Small Estate Affidavit is governed by Texas Probate Code Section 137. If you think you can prepare one then you don't need a lawyer's help. But, I doubt you can pull it off. You might want to look at http://www.co.travis.tx.us/probate/pdfs/small_estate_affidavit_checklist.pdf. This is not a form but will alert you to typical problems. Lastly, an annuity typically names a beneficiary. If you are the beneficiary then you should be able to claim the benefits with a death certificate and proof of your identity.
DISCLAIMER: This is not specific legal advice and does not establish an attorney/client relationship.
A small estate affidavit DOES NOT name an executor. Check with the financial entity before possibly wasting time on a process that may not meet your/their needs. Additionally, in some counties, like Jefferson, a small estate affidavit requires the appointment and expense of an attorney ad litem. This makes it almost as costly as actual probate naming an administrator/executor.
Kendall Cockrell is an attorney with The Cockrell Law Firm in Beaumont, Texas. None of the opinions he states on this site constitute an attorney-client relationship. For more information, contact The Cockrell Law Firm. Contact information available on Kendall Cockrell's profile on this site.