Yes, it is possible for your blood to show no ketones, while your urine does. This is because blood and urine ketone levels can vary independently of each other.
Blood ketones are a more accurate and reliable indicator of your body's ketone production because they measure the ketones that are actively circulating in your bloodstream. On the other hand, urine ketone levels can fluctuate based on how hydrated you are, how long it has been since you last ate, and other factors.
In the early stages of a ketogenic diet, it's common for the body to produce more ketones than it can use, leading to higher levels of ketones in the urine. Over time, as the body becomes more adapted to using ketones for energy, it may become more efficient at using them, resulting in lower levels of ketones in the urine.
However, this does not necessarily mean that your body is not in a state of ketosis. It's possible to be in ketosis even if your urine ketone levels are low or undetectable. If you're following a ketogenic diet and experiencing other signs of ketosis, such as increased energy and mental clarity, weight loss, and reduced appetite, it's likely that you are still in a state of ketosis, even if your urine ketone levels are low.