References are not obligatory. It is up to you whether you name referees in your CV. Your new employer can only contact them after you have agreed to this. Personal matters or reasons for resigning are not to be discussed in references.
If proof of good conduct is needed, it should be mentioned in the job advertisement.
When you leave a company, the employer must always give you a certificate. This may simply contain neutral content but must never say anything negative about your personality or your work.