release on his/her own recognizance(освободить до окончания следствия, получив от подозреваемого официальное обещание в письменном виде не выезжать из страны, города в течение оговариваемого срока to free someone from pre-trial detention with the condition that s/he not leave town)
be released on travel restrictions(освобождаться до суда под залог или подписку о невыезде = be released on bail or travel restrictions. He was held in detention for three days before being released on travel restrictions. | The fact that some senior Golden Dawn figures have already been released on bail or travel restrictions suggests the evidence may not be ... Alexander Demidov)