Texas requires most service businesses to collect and remit sales tax.
Below is the link for some detailed information-
I would suggest that you call the comptrollers office at 1-800-252-5555 and inquire about whether your specific service is required to collect and remit such taxes.
If the client is based in Ohio and the services are performed in Ohio than this would be an out of State service income and hence will not be subject to sales tax in TX.
Link to out of state sale-
Ohio does not charged sales tax on consulting services.
Link to Ohio sales tax on this service-
Let me know if you have any question.
Please note: This advice is provided with the understanding that all the relevant facts have been provided by you. Any change in facts might affect the advice given and hence may not be relied on in such cases. Nothing contained in this reply was intended or written to be used, can be used by any taxpayer, or may be relied upon or used by any taxpayer for the purposes of avoiding penalties that may be imposed on the taxpayer under the Internal Revenue Code of 1986, as amended.