If you are certain the oil is overfilled, then yes, this should be the problem. Single cylinder engines have little tolerance for excess oil in the crankcase. Since you're at it, you may as well change the oil in the mower while you have this all apart. In order to do this safely, be sure you have disconnected the spark plug wire from the top of the plug. You do not want the mower to start while you are under it. If you are unsure, ask someone who knows how to do this safely. You should also do this on a cool mower, as gasoline could leak from the tank or carburetor and pose a burning and fire risk. That said:
To change the oil on a single-cylinder lawnmower:
1) Gather materials.
--You'll need a pan or an old bucket to catch old oil, preferably one that has enough capacity for the old oil while also allowing the mower to be positioned with all four wheels on the ground.
--A set of wrenches or a socket set.
--Two fresh quarts of new motor oil of the recommended viscosity for your particular lawnmower.
2) Disconnect the spark plug from the ignition wire. You'll see a cable running to the top of the spark plug. Grab it firmly at the boot that sits atop the plug and pull firmly. If it doesn't come off easily, be sure you are pulling at the right spot.
3) Tip the mower either backwards or on its side and look underneath the cutting deck. Be careful, as gasoline may spill from the engine's tank. You should see a small square-head or hex-head plug directly below some point of the engine. That is the engine's oil-drain plug. CAUTION: You may need to rotate the cutting blade to gain access to this plug. Be aware that the blade can cut you and that if the mower starts now it can cause serious injury to yourself.
4) Locate the correctly sized wrench or socket that mates to the drain plug.
5) Using a correctly sized wrench or socket, carefully and slowly loosen the drain plug until it turns freely by hand.
6) Position your drain pan beneath the engine's drain plug.
7) Unscrew the drain plug by hand until the oil drains free. Setting the mower down on level ground with all four wheels will ensure the most old oil drains from the engine at this point. Go ahead and open the engine's oil fil cap at this time, as this also allows the oil to drain freely.
8) When the oil has stopped draining from the engine--usually a slow drip is ok--you can replace the drain plug by hand. Be sure the plug turns freely by hand--do not crossthread the plug as you will create a costly repair for yourself.
9) Tighten the plug snug--NOT samson tight--with the correct wrench or socket and wipe any oil present at the plug or surrounding area clean with a rag.
10) Remove the pan from below the mower and rest your mower on all four wheels.
11) Slowly fill the mower's cranckase to full with fresh motor oil. Often, less than a single quart is necessary. Go slow and do not overfill.
12) Tilt the mower backwards again and check for oil leaks at the plug. You may need to snug up the oil drain plug one more time before the first after-oil-change start.
13) Lower the mower, reconnect the spark plug, and start the mower. Let it run for about a minute and listen to the mower for any "bad" sounds. If you hear anything out of the ordinary, shut off the mower immediately and recheck the mower for abnormalities.
14) Shut the mower off.
15) Check the oil level. You may have to top off the fluid level again, as running the engine tends to let the fluids settle out.
16) Disconnect the spark plug once more.
17) Tilt the mower and check the drain plug one more time for leaks. Snug it up as necessary.
18) Let the mower back down to the ground and reconnect the spark plug to the ignition wire.
You should be ready to mow again. Remember to be aware of any oil drips as push the mower around after a recent change--that may indicate the plug is leaking. There is a great picture of what a mower's drain plug looks like in the link below. Just scroll down to the part where you see the picture labeled 'oil drain plug.'
--Hope this helps, Joe.