Criteria to prove no significant difference on duplicate sample

I am not informed about the details related to your method so I can only reply with a general comment. It all depends on the of the duplicates, the purpose of your method and the type of test that you perform.  The variation (imprecision) between duplicate results of a sample tested at the same time should be smaller than the longer-term imprecision of your method. What method performance is needed (e.g. sensitivity of calibration curve and long-term precision) must be based on client requirements and capability of the method. For example, the reason for duplicates, and acceptable level of imprecision and target measurement of uncertainty could be influenced by the sample matrix. The target performance either comes from your standard method, sector regulations or is established during method validation. 

I suggest you look at resources related to your sector and basic statistical guidelines. For example, the Eurachem guidelines, available at https://www.eurachem.org/index.php/publications/guides are useful to assist with analytical measurement evaluation.