It was, though very restricted one. Local authorities need to have money in order to do something useful for their town. Though local authorities hardly ever had personal funds. The taxes paid by the enterprises and people who worked there were almost in full amount transferred to the state treasury in Kyiv. Then in Kyiv, officials decided to whom and how much money to allocate. Often, the decision whether to give money for the local needs was made through the "kick-back" at all levels – in ministries, oblast and rayon administrations.
In fact, there was not a self-government, but a corrupt hierarchy line in Ukraine. It was strengthened every year. Therefore, local self-government could act contrary to the system (if it could act at all), and not due to it.