I think you should use "to do".
'do' is an auxillary, action verb: "you need to do [the thing]".
I have never hear a native english speaker use the: "I need do something." form.
Auxiliary verbs add functional or grammatical meaning to the clauses in which they appear. They perform their functions in several different ways:
By expressing tense ( ...
This appears to be a case of inadvertant misattribution by the Original Poster. Here is the actual text and its context:
The Cambridge Grammar of the English Language, Huddleston & Pullum (2002, p. 198)
As can be seen, Huddleston & Pullum are of course saying that such a sentence is perfectly fine. However, they note that we're unlikely to see this ...