In the federal government, you are REQUIRED to reset passwords once every 90 days (or sooner). Each time you do, you must write down the password, then wrap it in opaque construction paper or something similar, put it in a security envelope heavily wrapped with tape, and hand it to your department's security officer delegated for that function. There are other ways to do that if you have the ability to send secure e-mail, but the bottom line is that a regulation explicitly defines and requires a procedure to prevent exactly that occurrence.
(I was a U.S. Navy sys admin from 28 years, know that particular rule by heart.)
ask your boss for it
They may be trying to tell you something.
You're going to have to tell us what application you're talking about.
A safe bet would be to go to the software vendor with proof that you're an authorized party to the company (usually tax information or something) and ask them if they have a tool to change the account password.
From this point forward, it should be clear that no soul person should have this access in case of emergency.