He was killed then put over the bath. Shirt is pulled up where he was lifted, no blood on back of neck/shirt from head laceration, no bruising under chin, etc..... Then again, he may not be dead, still blood running from his nose.
It does look like he slit his wrists, maybe the laceration to his head and the bruising on his face was because he fell? May he couldn't get up enough nerve to kill himself so he got drunk and fell before he slit his wrists.