Table VI, Law VII says:
Where anyone demands freedom for another against the claim of servitude, the Prætor shall render judgment in favor of liberty.
What this actually means is that if a free person (citizen or otherwise) was wrongfully held as a slave, a friend could go to the Praetor to seek their release. Note that this was basically a civil trial, and the slave owner would be able to put forward a legal defense. It fell to the Praetor to determine if the purported slave was in fact legally free or not.
Therefore, the law did not help the average slave. Note that they could not simply go to the Praetor themselves, and would instead need someone plead their case. Even assuming that a champion could be found, there was no reason to expect that they could prevail against the slave owner. At least, not if the acquisition was made legally.
Of course, [Table VI Law VII] does not help an already establihed slave, but it prevented unethical men from forcibly enslaving others.
- Newton, Michael. The Path to Tyranny: A History of Free Society's Descent Into Tyranny. Michael Newton, 2010.
On the other hand, the law gave rise to a loophole for freeing slaves, by having someone go to the Praetor and argue a slave was wrongfully held. The owner could then deliberately throw the case, allowing the slave to be declared free.
A person who wished to free his slave would arrange for a friend to bring against him the vindicatio in libertatem, the claim for freedom, before the preator. The friend thus claimed that a free man was being wrongfully held as a slave, the owner put up no defense, and the praetor declared the slave free.
- Watson, Alan. The Spirit of Roman Law. University of Georgia Press, 1995.
As tohuwawohu pointed out, this law doesn't appear in some versions of the Twelve Tables. It is worth noting that the original Twelve Tables were long lost in antiquity, and any modern rendition are in fact reconstructions based on quotes or paraphrases in other sources. For the vast majority, the table number is unknown. The organisation by table is thus a modern categorisation of convenience with little more than educated guesswork.
All this is to say, there is a great deal of uncertainty in the exact form of the Twelve Tables. It is indeed possible that this specific law did not actually exist, though I have no specific reason to doubt the edition TheHonRose cited. Assuming it is correct, the interpretation in this answer is I believe valid.