What you do with income such as dividends and interest with the States is:
Allocate some to each state. If paid throughout the year (which most are) then allocate it by time in each state.
I see 4 months (1/3) for one state and 8 months (2/3) for the other. I do not see a filing requirement for VA unless you have VA taxes withheld and then would file a return with no income to get the money back.
See below:
https://www.tax.virginia.gov/who-must-file
