The fact that you deal with the same study population means that you have the right to show information about the population just as much as in both studies. To cite the other study, particularly the table, is perfectly fine. But, if the table is key to the paper, for example, in the methods section, it seems more appropriate to include the information in your new paper. It is also perfectly fine to reproduce the table just as you can reproduce a figure from another paper but then the table might include or lack information that is superfluous or needed, respectively in your new study.
I would therefore suggest that you create your own table and format it to suit your purpose best. You should also cite the other study and state that your new study is based on the same study participants as the previous study and then also refer to both tables to indicate the kinship. That way it is obvious that you are not trying to conceal that the tables contain the same information but that the information is key for both studies. It should be clear to the reader that there is a common basis for the two studies.