They may be doing this as a way to setup direct deposit, or to scam you. Do a search for the company through the BBB, type in the company name followed by "scam", just enter the company name into google and see what comes up. At a MINIMUM to release account information to an employer like this you should find a few things.
1. Where their corporate headquarters are located.
2. They should have a legtimate website for customers to view (and yourself)
3. There should be legit company emails (do not do business with an employer that uses (@yahoo.com, hotmail, gmail, etc.). A real company will have their own email address.
4. Ask if they have the option to send you a regular check first. After that posts and clears, you will provide the information.
5. If it is an "industry leader" verify that. You can do this because most "industry leaders" are publicly traded companies. Hit the stock market sites like cnbc.com, msnbc.com, cnn.com, wsj.com and so on.
6. Trust your gut. Never go with something you are not comfortable with.