Hi Cindy, apologies for the delayed response. We're working on finding the right expert for your question and should have an answer soon. 

Good Evening Cindy,

After reading your question I am assuming that you have positively identified the plant as Poison Hemlock. It looks like Queen Anne's lace but has purple "splotching" and smooth hollow stems.  If not positively identified when it comes up again you can take a sample to the OSU Extension Office located at 2055 Reading Road, Suite 500, Cincinnati Ohio 4520<personal data hidden>. 

I researched what has been studied regarding the toxic plant in Ohio and neighboring states. I have not found any scientific studies or evidence that the plant leaves any toxicity in the soil. As suggested by a Certified Horticulturist in Maryland, "removal should be sufficient. If in doubt, you can only plant non-root crop vegetables in that area." Monitor the area for a few years for new Poison Hemlock plants.  

Assistant Professor Joe Boggs with OSU Extension pointed out that the seeds from one growing season of Poison Hemlock may remain from 4-6 years so keep a close watch of the area. If more appear and you decide to use herbicide on new sprouting plants check the label on the container for how long you must wait before planting. Most say 3 - 4 days but there is no uniform guidelines.

http://bygl.osu.edu is a great resource during the growing season. It is a free subscription newsletter that gives current research on yard, garden and landscape information. There have been a few newsletters on Poison Hemlock.

Another great resource is https://ohioline.osu.edu that contains numerous fact sheets that you can read and print off on a myriad number of agricultural subjects.

I hope I have been helpful and not too chatty. 

Happy Gardening, 

Mike Heys, Franklin County Master Gardener