Instance/object variables can be defined outside a constructor if something approaching the flyweight pattern is adopted...

package MyPkg;

my @Instances; # Visibility restricted to package by lexical declarati
+on

sub new {
    my $self = shift;
    my $opts = ref $_[0] ? shift : { @_ };
    push @Instances, { %$opts };
    return bless \(my $me = $#Instances), $self;
}

sub getScore {
    my $self = shift;
    return $Instances[$$self]->{score};
}
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As for class methods, all subs declared in a package are, by definition, class methods since the package is the equivalent of a class. The invocation context is determined in the subs/methods themselves e.g.

package SomeClass;

sub classMethod {
    my $self = shift;
    die("Not an object/instance method") if ref $self;
    .
    .
}

sub objMethod {
    my $self = shift;
    die("Not an class method") unless ref $self;
    .
    .
}
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Once again, just my 10 penn'orth FWIW, hope it's of interest/use to you