Does multicolinearity of variables imply complementary inputs? I've been thinking about how to answer this question How to econometrically identify perfect complements in production? and may think that multicollinearity has something to do with identifying such a process.

If I have a regression such that:

$$y=\beta_0+\beta_1x_1+\beta_2x_2+\mu$$

where $x_1$ and $x_2$ are correlated with each other. 

does that imply that some function of the nature $\min\{x_1,x_2\}$ is present in the determination of $y$?
A Leontief production does imply perfect multicollinearity between the inputs, since there is no substitutability between them. Thus, if a firm's production technology features non-substitutability between inputs, one would observe the firm choosing inputs in fixed proportions. 

However, (perfect) multicollinearity does not necessarily imply non-substitutability. For instance, the Cobb-Douglas production technology of the form $y=x_1^{0.5}x_2^{0.5}$ is also consistent with a firm choosing inputs in fixed proportions. So the answer to your question is no (from a theoretical perspective).