An asyncio SSL server frequently sees duplicated connection_made() calls for an incoming SSL connection.  It does not happen to all SSL connections; perhaps 10-25% of them.  It never happens to TCP connections. 

Here are some examples of logs from one I run.  I see this on MacOSX and DragonflyBSD, others have reported the same on Linux, so I believe it's a quirk in asyncio and not O/S specific.  I assume it is a bug in the wrapping of the raw TCP transport with an SSL one.

2017-04-20 07:22:44.676180500 INFO:ElectrumX:[14755] SSL 218.185.137.81:52844, 256 total
2017-04-20 07:22:45.666747500 INFO:ElectrumX:[14756] SSL 218.185.137.81:52847, 256 total

The log is output on a connection_made() callback to a protocol, and not from the protocol's constructor.  They are very close together, from the same IP address and ports that are close together.  The first connection was closed with connection_lost() before the 2nd connection_made() because the total session count (here 256) did not increase.

Here is another section of my log with 2 more examples.  Totals are not monotonic because of course disconnections (not logged) happen all the time.

2017-04-20 07:30:31.529671500 INFO:ElectrumX:[14796] SSL 193.90.12.86:42262, 259 total
2017-04-20 07:31:04.434559500 INFO:ElectrumX:[14797] SSL 70.199.157.209:10851, 259 total
2017-04-20 07:31:05.765178500 INFO:ElectrumX:[14798] SSL 70.199.157.209:10877, 259 total
2017-04-20 07:31:32.305260500 INFO:ElectrumX:[14799] SSL 64.113.32.29:35025, 256 total
2017-04-20 07:31:44.731859500 INFO:ElectrumX:[14800] SSL 188.107.123.236:60867, 255 total
2017-04-20 07:31:45.504245500 INFO:ElectrumX:[14801] SSL 188.107.123.236:60868, 255 total
2017-04-20 07:31:48.943430500 INFO:ElectrumX:[14802] SSL 136.24.49.122:54987, 255 total
2017-04-20 07:31:59.967676500 INFO:ElectrumX:[14803] TCP 113.161.81.136:2559, 256 total
2017-04-20 07:32:03.249780500 INFO:ElectrumX:[14804] SSL 69.121.8.201:63409, 256 total

Another reason I believe this is an asyncio issue on the server side is that someone else's server software that doesn't use asyncio logs in a similar way and does not see duplicated incoming "connections".