Welcome to the Senior Health Forum. You've asked a very interesting question. I am far from and expert. However everything I read tells me the answer to your question is yes. Low testosterone levels can cause depression at any age.
However depression in senior citizens can have many other contributing factors not associated with testosterone levels. Loss of career, a mate, loss of friends, decline in health, loneliness and many other age related issues can cause depression. I don't know the reason for your question but consider all the factors when making your assumption.
Best of luck to you.
Mount Sinai Hospital is currently conducting a clinical trial involving use of a transdermal testosterone patch for those over 65 that should provide a definitive answer to your question.
The answer right now is "possibly".