No, to my understanding, "me too" would be an unusual response to most negative sentences.
We normally answer with a negative construction when we are confirming negative questions, and with a positive construction when we are in confirming positive questions. This can lead to cases that may seem illogical, but are nonetheless considered correct.
For example, let's say that Person A were to ask, "Aren't you coming?" Person B might respond, "No, I am not coming." This is, strictly speaking, a double negative, but is generally considered the correct form. I'm not sure why the language works this way -- it may be a holdover of negative concord, which was normal in Old and Middle English, but uncommon today.
Back to your question, let's say that Person A were to say, "I can't understand it." Person B, if expressing agreement, might respond, "Me neither." If this were a positive expression, Person A might say, "I understand it," to which Person B might respond, "Me too."