This is a great question that I think you should bring up to the US Census bureau.
I believe at one point they did explore how to come up with capital measures by state; however, nothing ever happened. At this point and at the time of this posting the measurement of capital measures by state does not exist. It would appear this would be the "Holy Grail" of economic measurement.
There may be some capital data on equipment and structures at the state level from the Survey of Manufactures data (ASM) from the census bureau but that would be for only one sector in the economy.
There have been some studies about state level investment but the data used for the analysis are mostly state shares from aggregate US totals. The ratio used to come up with these types shares usually comes from the researchers assumptions, which is best practice available.
Below is an example of a report:
If there is capital data at the state level. Someone please post the source here.