Could research data fall under the Freedom of Information Act?
The original Freedom of Information Act applied only to information in the possession of government agencies. That means that the release of reports and proposals submitted to the funding agency could be compelled under the FOIA. But it did not apply to data from the research, if in possession of the PI and not the funding agency (as is typically the case).

A later amendment (Shelby amendment) expanded the FOIA to apply to some federally funded research data in the possession of a non-profit institution, as follows:


The release of "research data relating to published research findings produced under an award that were used by the Federal Government in developing an agency action that has the force and effect of law" may be compelled under the FOIA, if
the data is not "trade secrets, commercial information, materials
necessary to be held confidential by a researcher until they are published, or similar information which is protected under law."


Also, the requestor may be charged a "reasonable fee equaling the full
incremental cost of the agency, the recipient, and applicable subrecipients."

So the general answer to your question is that in most cases, the FOIA does not compel the release of data from federally funded research.

Regarding state law, it seems from the appendix to this report mentioned in another answer that at least one state does have an open records statute that may apply to research data produced by employees of the state university system:


  "Measuring Reproducibility in Computer Systems Research." Christian Collberg, Todd Proebsting, Gina Moraila, Akash Shankaran, Zuoming Shi, Alex M Warren. March 21, 2014.