Generally, you become a resident of a state when you relocate
- your place of sleeping,
- your mailing address,
- your driver's license,
- your voter's registration,
- similar things like landline phone
to a location in that state. Thus, if you rented an apartment in Texas prior to buying the home and got a PO Box for mail in Texas, that could be a sign of residency.
However, each state has its own definition of residency (or none at all); thus, you could literally be a resident of two states at once, under their differing rules.
Please see this Ohio web page on the residency issue. It's for non-residents, but it gives you an idea of what Ohio is looking at to define residency.
