This should rarely happen. If it does happen and that there is no way you 
can identify one particular newsgroup, you may wish to do the following :

 1)  Decide which newsgroup is subscribed by the audience to whom
     you want to target your post. 
 2)  Then, send the post to both newsgroups.
     Mention in which newsgroup you wish to discuss this thread
     in the future.
     Set all follow-ups of the post to the newsgroup in which you 
     want to discuss this thread. 

For example :

  Subject: Is Cruise any good in Vampire ?
  
  Content : The poster could possibly be a fan of Tom Cruise
            and would like to know if he was good in the 
            film _An_interview_with_the_Vampire_. The main
            interest is Tom Cruise. IF the time of the post
            happens to be when the film has just been released, 
            only people who have seen the film will be able to 
            answer that.

  Solution :  Post to rec.arts.movies.current-films 
              and rec.arts.movies.people
             
              set follow-up to rec.arts.movies.people
              (i.e. in header, put, Followup-To:rec.arts.movies.people)

  NOTE : If the film involved in a similar example has been out
         for quite sometime (i.e. if it is a past film), many 
         people would have seen the film and you would 
         only need to post it to rec.arts.movies.people.

  The bottom line is : 
  Post it to the most appropriate newsgroup.
  There is NO NEED to crosspost it to both groups. With
  as many newsgroups as there are, nearly no postings belong in more
  than one!