I think its pretty safe. I don't think bank transfers are reversible.
WRONG! Yes, they are.
OP, if they're making a "cash" deposit into your account, how could one, to include the bank, tell whether the cash was obtained illegally? The safest bet is to have the buyer physically go to your bank and make a cash deposit. I wouldn't trust wires or transfers of any kind.
For example if someone were using obtain the ransom obtain from kidnapping and somehow police found out part of the money been moved into my account. I might be thinking too much but i just plan to play safe..