I believe that you're completely wrong in stating this,
Jimbo
...Its a bit complicated by the fact you have rented a house but in effect you are a tourist and should not have to report to the police...
My understanding is that
every foreigner in Indonesia needs to be "reported" to the police. For tourists staying in hotels, this is done automatically by the hotels so the guests are seldom aware of the process. Even staying overnight somewhere else requires the owner of the premises to make a report. (Naturally enough, this is often ignored but technically "illegal".)
The reason? Just think about it. For example, a tourist arrives in Indonesia and books into a hotel. A few days later finds the tourist at some other location, maybe at a party. Could be some local affair, (like a
bazaar), maybe an expat's villa, whatever. The tourist crashes the car/motorbike, gets sick and dies, drowns somewhere...How will the police know who the tourist was?
mimpimanis rightly pointed out that
...the owner of the house should report your arrival. It is their responsibility...
She also mentioned the point that
...the owner may not know about this, or want to be bothered...
Probably the latter, "being bothered". Many Indonesians would rather not have to go to a police station to fulfill their legal "responsibility".
In my own case, I always report/re-report myself after being out of the country for
any length of time. How much it costs depends upon who is on duty at the time. I've paid between
Rp 20,000-50,000 for a year.
The funny part is that it would take
very Wild Horses to get my Balinese landlord to do his "duty". I do it for him. Without fail, he's on my doorstep the very next day asking for a photocopy of the report...
8)