Should I use 'or' or 'nor' after a negative statement?

If the two options are negative (neither this nor that) then use "nor". Otherwise, use "or". Your example sentence can be reworded to read, "This document covers neither the SDK interfaces nor any other reference material."

NOTE: In my experience, Word's grammar checker is mediocre at best. It has a tendency to look at a sentence and suggest the opposite of the correct word. It was especially bad with [your/you're] in versions up to and including 2003, so I just keep it turned off and rely on thorough proof-reading.

My ear agrees with Word on this one. Two other possibilities:

"This document covers neither the SDK interfaces nor any other reference material."

"This document does not cover the SDK interfaces, nor does it include any other reference material."

My guess is Word interprets this as:

This document does not cover [either] the SDK interfaces or any other reference material.

Compare:

• I don't study French or Spanish. [Equivalent to Word's preference].
• *I don't study French nor Spanish. [Equivalent to your sentence].
• I study neither French nor Spanish. [Equivalent to moioci's first rewrite].
• ?I study neither French or Spanish.

According to Grammar Girl and her references used, your original sentence is correct, because your direct objects (ie the SDK interfaces,any other reference material) are noun (phrases):

When to Use “Or” Instead of “Nor”
“Neither” and “nor” are bosom buddies. They require balance.

In all our examples so far, we’ve used “nor” to indicate a negative state that continues after something else negative happens. However, when the second negative item is a noun, adjective, or adverb phrase (4), you should use “or” to continue the negative thought because according to Bryan Garner “the initial negative carries through to all the enumerated elements” (5). For example, when you use the word “not,” the structure “not A or B” is correct. You’d have to say, “He is not interested in math or science”; “He is not interested in math nor science” won’t work. Likewise, “She didn’t speak slowly or clearly” has a better ring to it than “She didn’t speak slowly nor clearly.”

[BUT] When to Use Either “Nor” or “Or”

If, on the other hand, the second part of the negative is a verb phrase—not a verb clause—then you can choose to use “nor” or “or” (6). Both of the following sentences will work: “Santa will not permit naughty behavior or even consider bringing presents.” “Santa will not permit naughty behavior nor even consider bringing presents.” You as the writer get to decide which one sounds better. If you’re unsure which word to use, or if you want to avoid the problem, you can try saying, “and no” for the second part of the negative (7): “I have no time and no money.” The phrase “and not” will also work: “Santa will not permit naughty behavior and will not even consider bringing presents.”