A \({2-rainbow\; dominating\; function}\) of a graph \( G \) is a function \( g \) that assigns to each vertex a set of colors chosen from the set \( \{1, 2\} \) so that for each vertex \( v \) with \( g(v) = \emptyset \) we have \( \cup_{u \in N(v)} g(u) = \{1, 2\} \). The minimum of \( g(V(G)) = \sum_{v \in V(G)} |g(v)| \) over all such functions is called the \({2-rainbow \;domination\; number}\) \( \gamma_{r2}(G) \). A \(2\)-rainbow dominating function \( g \) of a graph \( G \) is independent if no two vertices assigned non-empty sets are adjacent. The \({independent \;2-rainbow\; domination\; number}\) \( i_{r2}(G) \) is the minimum weight of an independent \(2\)-rainbow dominating function of \( G \). In this paper, we study independent \(2\)-rainbow domination in graphs. We present some bounds and relations with other domination parameters.