"He´d rather not to say anything then."   Note my addition of "to".

There is little difference in meaning between this and "He prefers/chooses  not to say anything then." 

This is present, not past. 

To express the past, I would suggest "He chose not to.." or "He preferred not to..."

Let's try a different verb.  How about "how"?  I'd like a glass of water.  Past or present?  Present, of course.  I'd prefer a glass of water to a glass of milk.  Past or present?  Present.