It seems clear that the tower and the palantír were connected in an important way. In Appendix A (I, iv) to The Lord of the Rings, it is said that, '...the Tower of the Dome of Osgiliath was destroyed, and the palantír was lost in the waters.' That seems to clearly imply that the fall of the tower directly caused the loss of the Seeing-stone (and earlier editions actually used the phrase 'Tower of the Stone of Osgiliath' in this passage).
Even as amended, this statement does not square easily with the claim made elsewhere that the palantír '...was under the Dome of Stars at Osgiliath before its ruin' (The Two Towers III 11). If the tower fell, why should the Stone be lost if it was held beneath the dome? The most likely explanation seems to be that the dome was a part of the tower (in which case we would need to imagine the tower as a very large, broadly based structure in order to hold the hall of the Stone).
An alternative possibility is that the palantír was moved from its normal location beneath the dome during the siege, and taken to the nearby tower for safekeeping. Certainly we know that the Stone was lost in the Anduin, implying that it must somehow have been taken or dislodged from its usual place beneath the dome, but there's no direct evidence to support this alternative idea.