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.
One of the most important parts of a college application is the personal statement, a one_ to two_ paragraph description of anything relating to you and your application. Sometimes, personal statements are optional; other times, they take the place of essays. Regardless of whether they're required or not, you should always take advantage of the opportunity to construct a well thought_out description of why you'd make a great addition to the incoming class.