Google says the state line runs down the middle of State Line Road. OSM says the state line runs on the east-side ROW of State Line Road.
I would trust Google on this more than OSM, the boundaries in the US (especially in the Midwest) are not the most accurate (have been working on updating/fixing the admin boundaries in SD for the last three years almost). It's not like MODOT stops maintaining the road 20 feet before the intersection or whatever the discrepancy is anyway, any sort of project (snow removal, new pavement, etc.) will end at the State Line Road intersection because it's easier to set the construction limits.