Is this a DUI case?

Police report states as follows.. I was dispatched to a call for a crash with injuries at SB SR 9a and SR 9. After arriving on scene, there were two sheriffs deputies on scene a white male was sitting on the light pole that a been struck. Green Honda civic was sitting in the ditch with a white female later identified as the mother and owner of the vehicle that had struck the light pole. I was notified by officer that the driver (my name) admitted to him that he was driving the vehicle. I obtained a printed copy of his Drivers license from officer and the drivers license of the passenger of the vehicle. I asked the white male what happened, he looked at me with a blank stare and didn't answer. I asked the mother of (my name) what happened she stated he was driving south on sr 9a and then he struck the guardrail and then hit the light pole after diving crazy. I then asked her who was driving she stated that he was,(my name). I then asked her if she was drivng she stated no it was (my name). I then returned to (my name) and asked him to stand up he fell over backwards in the grass. he was very unstable. I smelled a strong odor of alcohol coming from his breath. I then asked him what happened. he stated that he didn't know what happened. I then asked him was he driving he stated that he wasn't driving it was his mother. I then asked him what happened while she was driving. He stated that he didn't know. I then told him I was no longer conducting a crash investigation and that I was now doing a DUI investigation. I read him Miranda. He stated that he understood his rights and that he would talk to .I asked him had he been drinking. he stated that he wasn't drinking . he was very unsteady on his feet. I then asked him what happened again he stated that he didn't know. I then asked him if he would submit to field sobriety exercises. He stated no. I then placed him under arrest for DUI with property damage .