Power of the police to arrest a person depends on the nature of offence committed by him. Such power is given, mainly, under Section 41 of Cr.P.C. Generally speaking, the police has the power to arrest if a cognizable offence has been committed by an accused person. Recent changes in Section 41 Cr.P.C. have put some more restrictions in the power of arrest of police even in respect of a cognizable offence if the punishment in the offence is up to 7 years' imprisonment, though the power to arrest in such a case also still remains available to police (though subject to more conditions now).
The power of arrest is available to police irrespective of whether or not they have issued summons to you. Even in the absence of issuing summons, the police may have the power to arrest if other conditions are satisfied as mentioned in Section 41 Cr.P.C. This power is dependent on the nature of the offence and the need for arresting the accused for the purposes of investigation or to ensure that he does not escape, etc.
You have not mentioned the nature of offence in your case, therefore it is not possible to give a specific answer to your answer.