Is having an identical twin reasonable doubt in a murder case?

Lets say that there are identical twins that live together. They have many articles of clothing in common and share most of their belongings, but sleep in separate rooms. One gets out of bed, gets dressed, leaves the house on foot and commits a murder by bludgeoning the victim with a baseball bat, spattering blood all over themself and leaving behind eyewitnesses, surveillance footage, shoe prints, and DNA footage placing themself there.

He/she wipes clean the murder weapon of finger prints and drops it. Then the twin walks home, undresses and thoroughly scrubs in the shower and sneaks back to bed.

In the morning one of the twins calls the police saying that they found the bloody clothes, confronted their twin about it, and that their twin more-or-less confessed to murder. The accused twin claims that they had not noticed the clothes in the bathroom and that the alleged conversation never happened prior to the police being called. Both use the identical alibi of being home asleep and knowing nothing about the murder. Both claim to have worn the discarded clothes recently, but not on the night of the murder. Both claim to have showered shortly before going to bed that night. Both have equal motive for the murder.

Do you think that there would be enough forensic evidence to determine which of the two had actually committed the murder? How would this case play out in a trial?