The answer to this hinges on what is meant by "the same". If the gist of the poster is the same as that of the full conference paper, this would be some kind of double submission, which is usually not acceptable.
Posters can, however, be, and at least in my CS subfield, routinely are, complementing the paper by focusing on aspects of the same research endeavour that are more suited for a poster, such as:
- a test prototype, which is only a side-note in the main paper, can be in the focus of the poster
- the generic methodology used for an evaluation; while the paper might be describing the concrete case in order to focus on the problem, the proposed solution, and the results, the poster can be used to document details about the evaluation of the solution and instruct others how to use the same method for other, similar problems (usually too far out of scope to fit in the main paper, and too "thin" to warrant a regular paper of its own)
- possible future work building upon your paper, in order to incite a discussion during the poster session, gather new ideas, and taking advantage of the circumstance that poster sessions often explicitly invite work in progress
In any case, you should reference the poster from the paper and vice-versa, both in the papers and during the conference, to avoid allegations of self-plagiarism, and even more importantly, because you want to make sure people who are interested in your research are aware of both published facets thereof.
If you have an opportunity to inform the conference chairs about the way in which your submissions are linked, it cannot hurt to do so, but this is not always possible or even customary in some fields.