Please re-state your question again.
Right now bank order the appraisal. If you do the no point, no fee re-fi, loan agent shall cover (meaning will mail you a check for the appraisal fee amount AFTER re-fi is closed) this.
BUT, if you switch from one lender to another lender for the same re-fi case, you have to pay appraisal fee twice. Again, it is up to your loan agent willing to cover you both or not.
I am not sure I answered your question completely.