I have a professional service corporation in the financial industry. One of my clients for over 20 years is unable to communicate well and I needed to obtain some information from his annuity provider so, with his permission, i contact the annuity provider and i said i was my client. Well, they asked me some security questions which i could not answer and they have my phone number from caller ID. My question is whether i can get in trouble for contacting the annuity company and asking them questions on behalf of my client? I received his permission prior to calling, i am hoping there is no problem with me contacting the annuity company.

Thats fraud against the company, not the client. This happens all the time where i work. We catch people impersonating others trying to commit identity theft. So, i would be very careful as it could lead to criminal investigation. I know, i refer these types of cases out all the time.

That makes sense. What kind of trouble could you get into for impersonating another? Is there a federal or state law on that issue?

The crime of false impersonation is defined by federal statutes and by state statutes that differ from jurisdiction to jurisdiction. In some states, pretending to be someone who does not actually exist can constitute false impersonation.
I guess it depends who is being impersonated. In Texas, impersonating "a public servant with intent to induce another to submit to his pretended official authority or to rely on his pretended official acts" is a crime (Tex. Penal Code Ann. § 37.11 [West 1996]

I didnt impersonate a public servant, just a client. I was just trying to get information to assist with the maintenance of their accounts. And i had the client's permission too. Thats all.