If you are applying to several different schools using one generic statement will be easily recognized and just as easily dismissed. WHY _ because you will be seen as not making an effort sell yourself to this particular school, low effort equals low interest to admissions representatives. Remember the admission committee will likely view thousands of these statements from qualified candidates and they will spot a weakness, flaw or lack of attention to the process in a heartbeat. What you don't want to do is give this committee an easy excuse to dismiss your statement and application.
A great exercise to conduct before you begin to put together your admission essay is to start with a sample. This way you can see exactly what goes on a personal statement and you can also check out how the tone of the writer is and what they actually are emphasizing.