No, you won't have to pay capital gains tax when gifting this property, though gifting property to relatives - particularly rental property - frequently not the best thing to do from the standpoint of taxes.
You will need to file a gift tax return, (Form 709), as the gift exceeds the annual gift tax exclusion of $14,000 per year. However you almost certainly will not pay any gift taxes as the value of the gift is well below the current lifetime exclusion of $10.98 million for a married couple.
One problem with gifting property is that the donor's basis carries over to the recipient while inheriting property means that the recipient's basis becomes the property's full fair market value. So while the $382K current value is relevant for gift taxes it's irrelevant to the recipient's own income tax situation. Depending on the circumstances it could be worthwhile to consult with a local CPA to weigh the pros and cons of gifting the property.