That would be the same dimension as us... just a different neighborhood.
If the theories that there are a dozen or so dimensions to our space/time and that we can only see three of them (and experience a 4th, e.g linear time) are correct... then it is possible that life may exist in one of the other eight or so dimensions and we are simply incapable of detecting and/or interacting with it.
If the theories that there are a dozen or so dimensions to our space/time and that we can only see three of them (and experience a 4th, e.g linear time) are correct... then it is possible that life may exist in one of the other eight or so dimensions and we are simply incapable of detecting and/or interacting with it.