According to https://ncatlab.org/nlab/show/Atiyah+Lie+groupoid#idea *Atiyah Lie Groupoid* $At(P)$ of a Principal $G$ bundle $\pi:P \rightarrow X$ is a category such that $Obj(A(P))=\lbrace \pi^{-1}(x): x \in X \rbrace$ and $Mor(A(P))=\lbrace f:\pi^{-1}(x)\rightarrow \pi^{-1}(y): f$ is a $G$ equivariant morphism $\rbrace$. Structure maps of this category are easy to guess. Now it is easy to see that $At(P)$ is indeed a groupoid. 

Although it is mentioned in https://ncatlab.org/nlab/show/Atiyah+Lie+groupoid#idea that *Atiyah Lie Groupid* is indeed a Lie Groupoid but I am not able to guess  appropriate smooth structures on $Obj(At(P))$ and $Mor(At(P))$ such that the source and the target maps are surjective submersions and other structure maps are smooth. 

Is there any **natural choice** of such Smooth structures on both $Obj(At(P))$ and $Mor(At(P))$ such that $At(P)$ is a Lie groupoid so that if someone talks about *Atiyah Lie Groupoid* of a Principal $G$ bundle then he/she is precisely assuming **those natural choice of smooth  structures** on $Obj(At(P))$ and $Mor(At(P))$?

I would  also be very grateful if someone point me to any literature in this direction.

Thank you.