I suspect this exists, if anyone has a reference please that would be very helpful.


By signed graph, I mean each edge is designated either odd or even (e.g. as in Guenin's result for weakly bipartite graphs).



Is there a polynomial-time algorithm to check if a signed graph contains an odd-K5 minor?
Yes. This result is contained in my PhD thesis, which is available [here](https://uwspace.uwaterloo.ca/bitstream/handle/10012/4716/huynh_tony.pdf?sequence=1&isAllowed=y) (see Theorem 1.1.10). We prove that for any finite abelian group $\Gamma$ and fixed $\Gamma$-labeled graph $H$, there is a polynomial time algorithm to determine if an input $\Gamma$-labelled graph $G$ contains an $H$-minor. The case you are interested in is $\Gamma=\mathbb{Z} / 2 \mathbb{Z}$ and $H$ equals odd-$K\_5$. For signed graphs, this result was also obtained independently by [Kawarabayashi, Reed, and Wollan](http://wwwusers.di.uniroma1.it/~wollan/PUBS/parity_minors_web.pdf) (although I am not sure that a journal version is available yet). 


