You can use the -f operator to check if a file exists. (See perldoc -f -X for information on all the filetest operators.

sub connectdb { 
  die "Database file does not exist" unless -f "as2con.db";
  my $dbase = DBI->connect("dbi:SQLite:dbname=as2con.db", 
"", "", {PrintWarn => 0, PrintError => 0});
  return $dbase;    
}
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By the way, module names should start with an uppercase letter. Lowercase module names are reserved for Perl pragmas.