For example, I washed myself is Jau hai ma lavà "I have me washed"; based on French, I would have expected something along the lines of Jau ma sun lavà "I me am washed".
It turns out that you may place the object pronoun before the auxiliary (Jau ma hai lavà), as in (IIRC) Ladin [i.e. Vallader/Putèr], and you may use "to be" as the auxiliary (Jau sun ma lavà), as in Sursilvan, but the combination of both changes is not mentioned, and the "default" or neutral word order is the one I described first.
Then I thought about it from a German perspective, rather than a French one, and it seemed a lot more natural to me: Jau hai ma lavà is exactly parallel to Ich habe mich gewaschen, in both word order and choice of auxiliary!
Another little curiosity that RG shares with French is that the past participle has to agree with the subject in gender and number if you use the auxiliary "to be"* -- except if you add an object.
So a woman might say Jau sun ma lavada "I washed myself"/"Je me suis lavée"/"Ich habe mich gewaschen" but Jau sun ma lavà ils mauns "I washed my hands"/"Je me suis lavé les mains"/"Ich habe mir die Hände gewaschen".