When a portion of a contemplated parkway for the connection of two established parks or reservations is already a street, avenue or way, the care, custody and control of which has been transferred to a park commission, and a portion is not a street, avenue or way, the care, custody and control of which has been transferred to a park commission, the commission may, in laying out parkways and boulevards, pay for the construction and improvement of such parkways and boulevards, throughout their entire length, from any money which may be in its hands for the purpose of construction and improvement of parks and parkways without the necessity of assessing the cost of such construction and improvement upon the abutting property owners.