The Director General of Commercial Intelligence publishes monthly foreign trade (export & import) statistics, grouped by 1) commodities, 2) economic regions & 3) countries. As far as I know, they do not publish state level data for exports, imports,..
As far as I know, DGCIS compiles data on exports and imports from the customs data from the ports. So, a firm based in AP may be exporting its goods from the Chennai port just because it is closer. So, DGCIS may be capturing this as exports from the Southern Region, they may not be in a position to classify as an export from AP.
Similarly, a foreign firm wanting to bring in inward FDI may set up its administrative office in Delhi and register the FDI with the Delhi office of DIPP/RBI. But the firm may be planning to set up its plant in Haryana or UP. So here again attributing the FDI to a particular may be difficult. Please see page 3 of the attached document.
So one way forward would be to do some kind of survey, talk to the Industry associations, etc...
Exactly as mentioned in the previous answer, there could be cases for example, where a handicraft or marble exporter from Rajasthan may export through an export house / export commission agent / CHA located in Mumbai & such export may be recorded from Maharashtra & not from Rajasthan. This may lead to discrepancies & incorrect compilation of data. Am not aware of any mechanism to sort out exports according to their place of origin.