Does a business need to post a “do not sell” link if it does not sell personal information?

No.

The CCPA requires businesses that sell personal information to, among other things, explain that consumers have a “right to opt-out” of the sale,1 and provide a clear and conspicuous link on their homepage titled “Do Not Sell My Personal Information,” which takes the consumer to a mechanism that permits the exercise of the opt-out right.2  If a business does not sell personal information, and if the business affirmatively states that it does not sell personal information in its privacy notice, it is not required to provide a notice of [the] right to opt-out” or post the “Do Not Sell” link.3