As I wrote in the CB, I think File::BOM might be the way to do it. I'm still searching, but at least I've a working example that shows the error:

#!/usr/bin/perl

use v5.12;
use warnings;
use autodie qw( :all );

use File::BOM;
use DBI;

open my $h,'>:encoding(utf-8)','test.csv';
say $h qq<\x{FEFF}"foo","bar","baz">;
say $h qq<"1","2","3">;
say $h qq<"4","5","6">;
close $h;

my $dbh=DBI->connect('dbi:CSV:',undef,undef,{ RaiseError => 1, PrintEr
+ror => 0, f_ext => '.csv'});
my $sth=$dbh->prepare('select * from test');
$sth->execute();
while (my @a=$sth->fetchrow_array()) {
        say join(",",@a);
}
$sth->finish();
[download]

Update:

It seems that only the header() method in Text::CSV_XS is able to handle the BOM, and DBD::CSV does not call that method. Instead, it calls getline().

#!/usr/bin/perl

use v5.12;
use warnings;
use autodie qw( :all );

use File::BOM;
use DBI;
use Data::Dumper;

package My::Text::CSV_XS {
        use parent "Text::CSV_XS";

        sub DUMP
        {
                return Data::Dumper->new([\@_],['*_'])->Sortkeys(1)->I
+ndent(1)->Useqq(1)->Dump();
        }

        sub new
        {
                my $proto=shift;
                say "$proto -> new(",DUMP(@_),")";
                $proto->SUPER::new(@_);
        }

        sub header
        {
                my $self=shift;
                say "$self -> header(",DUMP(@_),")";
                $self->SUPER::header(@_);
        }

        sub getline
        {
                my $self=shift;
                say "$self -> getline(",DUMP(@_),")";
                $self->SUPER::getline(@_);
        }

        sub getline_hr
        {
                my $self=shift;
                say "$self -> getline_hr(",DUMP(@_),")";
                $self->SUPER::getline_hr(@_);
        }

        sub getline_all
        {
                my $self=shift;
                say "$self -> getline(",DUMP(@_),")";
                $self->SUPER::getline_all(@_);
        }

        sub getline_hr_all
        {
                my $self=shift;
                say "$self -> getline_hr(",DUMP(@_),")";
                $self->SUPER::getline_hr_all(@_);
        }
}


open my $h,'>:encoding(utf-8)','test.csv';
say $h qq<\x{FEFF}"foo","bar","baz">;
say $h qq<"1","2","3">;
say $h qq<"4","5","6">;
close $h;

my $dbh=DBI->connect('dbi:CSV:',undef,undef,{ RaiseError => 1, PrintEr
+ror => 0, f_ext => '.csv', csv_class => 'My::Text::CSV_XS'});
my $sth=$dbh->prepare('select * from test');
$sth->execute();
while (my @a=$sth->fetchrow_array()) {
        say join(",",@a);
}
$sth->finish();
[download]

>perl test2.pl
My::Text::CSV_XS -> new(@_ = (
  {
    "auto_diag" => 1,
    "binary" => 1,
    "escape_char" => "\"",
    "quote_char" => "\"",
    "sep_char" => ","
  }
);
)
My::Text::CSV_XS -> new(@_ = (
  {
    "auto_diag" => 1,
    "binary" => 1,
    "eol" => "\r\n",
    "escape_char" => "\"",
    "quote_char" => "\"",
    "sep_char" => ","
  }
);
)
My::Text::CSV_XS=HASH(0x23e04e8) -> getline(@_ = (
  bless( \*Symbol::GEN1, 'IO::File' )
);
)
DBD::CSV::st execute failed:
Execution ERROR: Missing first row due to EIF - Loose unescaped quote 
+at /usr/lib64/perl5/vendor_perl/DBI/DBD/SqlEngine.pm line 1480.
.

 at /usr/lib64/perl5/vendor_perl/DBI/DBD/SqlEngine.pm line 1271.
 [for Statement "select * from test"] at test2.pl line 71, <GEN1> line
+ 1.

>
[download]

Second Update:

There is an ugly way to get File::BOM into DBD::CSV. DBD::CSV inherits from DBD::File, and DBD::File has an f_encoding attribute that is simply wrapped in :encoding(...), without further processing. That string is then passed to binmode.

This is the relevant part of DBD::File:

sub apply_encoding
{
    my ($self, $meta, $fn) = @_;
    defined $fn or $fn = "file handle " . fileno ($meta->{fh});
    if (my $enc = $meta->{f_encoding}) {
    binmode $meta->{fh}, ":encoding($enc)" or
        croak "Failed to set encoding layer '$enc' on $fn: $!";
    }
    else {
    binmode $meta->{fh} or croak "Failed to set binary mode on $fn: $!
+";
    }
    } # apply_encoding
[download]

So, with a carefully crafted encoding string, it works at least on my system:

#!/usr/bin/perl

use v5.12;
use warnings;
use autodie qw( :all );

use File::BOM;
use DBI;

open my $h,'>:encoding(utf-8)','test.csv';
say $h qq<\x{FEFF}"foo","bar","baz">;
say $h qq<"1","2","3">;
say $h qq<"4","5","6">;
close $h;

my $dbh=DBI->connect(
        'dbi:CSV:',
        undef,
        undef,
        {
                RaiseError => 1,
                PrintError => 0,
                f_ext => '.csv',
                f_encoding => 'utf-8):via(File::BOM' # <-- this is the
+ evil trick!
        }
);
my $sth=$dbh->prepare('select * from test');
$sth->execute();
while (my @a=$sth->fetchrow_array()) {
        say join(",",@a);
}
$sth->finish();
[download]

Effectively, this calls binmode $meta->{fh}, ":encoding(utf-8):via(File::BOM)", and so, File::BOM can hide the BOM from Text::CSV_XS and DBD::CSV.

>perl test3.pl
1,2,3
4,5,6
>
[download]

Alexander