What do you mean by similar start and end dates? Similar to what? To another task? Or is it that the start date of that particular task is the same as the end date (which is very possible and allowed).
In the former scenario, if the other task should start at the same time of the task that you have, and if they are dependent on each other, then this is called start-to-start dependency, but, if they need to start at the same time, then the dependency is both start-to-start and finish-to-finish. I'm not sure how this can be done in MS Project.