Engorged tick fell off my dog. What to do now and did it lay eggs?

For the most part, ticks do not cause much harm, but do have the potential to transmit certain diseases and some can cause neurologic problems. Some of these diseases and complications would be obvious if they occurred already. It's good to clip the hair around where the tick was and examine the skin for any redness or swelling - this can indicate an infection. The vet can do some blood tests for the commonly transmitted diseases if necessary. However, it's likely that Pico will be completely fine.

Fully engorged ticks will lay eggs in the environment, so I would make sure to clean under any dark areas of the house.

Normal flea/tick medication can be given to kill other ticks and prevent any more from getting on him. I recommend the spot-on treatments like Frontline and Revolution. Your vet will be able to give you the best products, so I recommend waiting until Monday to get these.

In the meantime, you can give a bath. There are some flea/tick shampoos that you can get at the pet store. Just make sure you use it as directed by the manufacturer.

I hope that helps and all is well with Pico.