If you use a user DSN and then run the script as another user (e.g. with CGI): better use a system DSN if possible

But with access (and many other databases, you don't need a DSN in the DSN-Manager, just specify the file (with path) and the driver in your connect string, e.g.

my $DSN = 'driver=Microsoft Access Driver(*.mdb);dbq=d:\\path\\to\\dat
+abase.mdb'; 
my $dbh = DBI->connect("dbi:ODBC:$DSN", '','') or 
  die "$DBI::errstr\n";
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This and more is written in perldoc DBD::ODBC ...