There might be a clearer/cleaner way to get a single column back from DBI, using the built in DBI::selectrow_array "utility" method:

my $statement= q{
  SELECT COUNT(*) 
    FROM products 
   WHERE nr = ?
};

my $count = $dbh->selectrow_array($statement, {}, $nr);
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At first glance, you're probably thinking that this returns an entire array, and will just set $count to 1 no matter what (because you're expecting it to return a one element array). Though, after further inspection of DBI.pm, you'll see that this method checks wantarray to see how it should return. If it sees that you are asking for a single scalar and not an array, it will just return the first column, of the first row, and set $count to this value.

I think that DBI::selectcol_arrayref is better when you are returning one and possibly more rows, where each row should contain a single column.