Is it illegal for Chinese citizens to possess bows and arrows

It is not illegal to possess bows and arrows in China, but they are not to be used at will.

Administration of Public Security of the Ministry of Public Security: Non-mechanical bow and arrow equipment (recurve bows, compound bows) do not belong to the scope of management of the public security organs, and do not need to go through procedures with the public security organs for their manufacture, sale, purchase, possession and use.

Mechanical bow and arrow equipment, such as crossbows (also known as: mechanical crossbow, crossbow machine) is a strong lethal equipment, belonging to the state strictly controlled items.