1964 Chevy Impala no fire at the coil

Why would I have power at both sides what would need to be checked thanks

The + side of the coil should have two wires connected to it. A pink wire and a resister wire.
The - side of the coil should be connected to the distributor wire (black) that goes to the points.
The coil grounds thru the points, when the points open, the circuit is broken and the coil should fire.

So does that mean the points are no good they spark when the car turns over

The points do spark, A LITTLE. If you are seeing a large or brite spark, the condencer is bad.

Lets start at the begining.
A) Take the points out and look at the contacts. If they are blue or black, replace them. They should be a light grey color.
B) Put the points back in and gap them.017-.019.
C) change the condencer in the distributor.
D) if there is a condencer wired to the coil, disconnect it.
E) with the ign. Off, check the + side of the coil, there should be no power.
F) turn the IGN. To on, there should be power at the + side of the coil.
G) pull the coil wire off the distributor ( the fat wire that goes from the top of the coil to the center of the dist. Cap)
H) have someone crank the engine, while you hold the coil wire about a 1/4 inch from any grounded metal. (The intake is a good place) And you should see a brite bluish spark.
If not.
Check the coil with a ohm meter, remove the coil leads first. The coil should have contenuity between the + and - posts. If not, replace the coil.

In step E, if you have power at the coil, the wiring has been tampered with and you will need a wiring diagram to straighten it out.

Also. In step G, DON"T TOUCH the end of the coil wire while cranking.

One more thing, if there is any dirt or oil on the point contacts, you will not get a good ground to the coil and it will not fire when the points open.