It is really the landlords responsibility, however, an alarm is not an essential utility like gas water or electricity so I suppose he could that its not necasary for him to supply it in working order.
That said if the alarm was to fail and start sounding at silly oclock in the morning and you have no way of stopping it who is responsible then? If I was the landlord I would have had it removed before renting it out if I wasn't going to look after it.
If you as the tenant take on the responsibility you should get written permission from the landlord to cover yourself. Then you should call a few local companies and get some quotes to have it looked at professionally. I would recommend you use an accredited company or one that can be recommended by someone you know and trust. Dabbling with it yourself could end up with a lot of annoyed new neighbors, dont under estimate what could go wrong .