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If somebody says, "I feel sleepy," then another may say, "So am I." However, if the first statement is negative, can neither be used in replacement of so? If not, how should the second statement be constructed?
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IMO:

I feel sleepy
So do I.

I am sleepy
So am I.

I don't feel sleepy
Neither do I.


I would add:

I'm not sleepy.

Neither am I.
Thanks for the replies so far.

Saying "So am I" is just like saying "I am so," right? I just didn't think that neither can be used since it's a conjunction unlike so which is an adverb in this case so I don't know if it's ok to use "Neither am I" in formal writings.
The word neither is also used as an adverb, and there is nothing wrong with saying "neither am I".

He's not sleepy, and neither am I.

Hey, you all forgot about "Me neither"! But I remembered it, so what do I win? Emotion: smile
I don't like fried strawberries with onions and chocolate. - Me neither!
How about "either?"
NewguestHow about "either?"
No problem: Emotion: smile

He's not sleepy, and I'm not either.

Thanks for the replies. I just didn't think that "neither" can be used as an adverb too.
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