Sources tell Miller that Tsarnaev wrote the note in the boat he was hiding in as police pursued him, and as he bled from gunshot wounds sustained in an earlier shootout between police and his older brother, Tamerlan Tsarnaev Miller's sources say the wall the note was written on was riddled with bullet holes from shots fired into the boat. The shots were fired after Dzhokhar came up through the tarp covering the boat amid police fears that he had another bomb. Boston bombing suspect found hiding in boat View the Full Gallery » According to Miller, the note will be a significant piece of evidence in any Dzhokar trial -- it is "certainly admissible," and paints a clear picture of the brothers' motive, "consistent with what he told investigators while he was in custody," Miller said Thursday on "CBS This Morning." Miller explained that while Dzhokar admitted many of the same details to authorities, those admissions came "during the time he was interrogated but before he was given his Miranda warning." The note gives prosecutors supporting, clearly admissible evidence even if there is an fight over whether things he said before he was given his Miranda rights are admissible as evidence. Complete coverage: Boston bombings It took days to learn the identity of the bombers, and there was no official claim of responsibility, which is unusual in these cases. As investigators move forward with the investigation, "the last big question remaining is going to be who else knew anything? Is it going to be the wife? Is it someone overseas?" Miller said. The suspects didn't plan to stop after the Boston bombings, authorities say. They intended to go to New York City and set off a device or devices in Times Square. 41 Photos End game for Boston bomber suspect View the Full Gallery » The brothers didn't have well-developed plans for New York, but they still had intent, Miller said. So as Dzhokhar lay in the boat, he wanted to leave a message behind clearly supporting what the note says he and his brother had just done. For a plot as organized as the one was for Boston, it seems odd that -- with a choice of leaving behind a martyrdom video on a computer or a more formal claim of responsibility -- the brothers had nothing prepared, Miller said. A larger terror organization ensures that such videos are made out of the country and are ready to launch after the attack. So in the end, Miller concludes, the boat note was a way for Dzhokhar to get on the record as publicly claiming responsibility for the bombings. © 2013 CBS Interactive Inc. All Rights Reserved.