Context is important here; if it is a complete phrase (following either a question or a negative statement) then it has the meaning Imber Ranae and TropicalMontana have described.
A: "Has she had any problems with her computer lately?"
B: "Not that I know of."
"There aren't any bus stops on this street... not that I know of, anyway."
However, if it is the first half of a sentence rather than an answer to a question, the meaning will be different. E.g.:
"You can die from drinking too much water. Not that I know of anyone who actually died by drinking too much water!"
In this case, the speaker is adding a disclaimer about her first statement: She knows it is possible to die from drinking too much water, but she realizes as she says it that she might sound silly or like she is over-reacting, because she doesn't know about any time it actually happened.