Not 100% important pertaining to the Contact Form.
BUT, I forgot where I read this statistic but customers are more highly subjected to inquire more of a business, if there are some trust signals. Signals like SSL certificates, payment acceptance and yes, contact information.
Contact forms are not fully needed, but doesn't hurt if it is purely service based like SEO consulting. But you should 100% put your business address, phone number, and email on the front page, probably on the sidebar or header.