The answer is implementation specific.  You'll need to check tcp implementation header files on your OS.  Here is a sample client for linux that returns the socket state.
  ts = TCPSocket.new('localhost', 5777)
  ssl = OpenSSL::SSL::SSLSocket.new(ts, OpenSSL::SSL::SSLContext.new)
  ssl.sync = true
  ssl.connect
  # TCP_INFO is 11
  # note that TCP_INFO isn't defined in the ruby source.  
  # i had to look up the integer value in /usr/include/netinet/tcp.h
  optval = ts.getsockopt(Socket::SOL_TCP, 11) 
  state = optval.unpack "i" 
  puts "state: #{state}"
Here's the tcp_info struct for my up-to-date ubuntu linux
struct tcp_info
{
  u_int8_t      tcpi_state;
  u_int8_t      tcpi_ca_state;
  u_int8_t      tcpi_retransmits;
  u_int8_t      tcpi_probes;
  u_int8_t      tcpi_backoff;
  u_int8_t      tcpi_options;
  u_int8_t      tcpi_snd_wscale : 4, tcpi_rcv_wscale : 4;
  u_int32_t     tcpi_rto;
  u_int32_t     tcpi_ato;
  u_int32_t     tcpi_snd_mss;
  u_int32_t     tcpi_rcv_mss;
  u_int32_t     tcpi_unacked;
  u_int32_t     tcpi_sacked;
  u_int32_t     tcpi_lost;
  u_int32_t     tcpi_retrans;
  u_int32_t     tcpi_fackets;
  /* Times. */
  u_int32_t     tcpi_last_data_sent;
  u_int32_t     tcpi_last_ack_sent;     /* Not remembered, sorry.  */
  u_int32_t     tcpi_last_data_recv;
  u_int32_t     tcpi_last_ack_recv;
  /* Metrics. */
  u_int32_t     tcpi_pmtu;
  u_int32_t     tcpi_rcv_ssthresh;
  u_int32_t     tcpi_rtt;
  u_int32_t     tcpi_rttvar;
  u_int32_t     tcpi_snd_ssthresh;
  u_int32_t     tcpi_snd_cwnd;
  u_int32_t     tcpi_advmss;
  u_int32_t     tcpi_reordering;
  u_int32_t     tcpi_rcv_rtt;
  u_int32_t     tcpi_rcv_space;
  u_int32_t     tcpi_total_retrans;
};
You may note that my script only returns an integer.  Here's the C enum that details the TCP states and their integer values.  Again, this was found in /usr/include/netinet/tcp.h
enum
{   
  TCP_ESTABLISHED = 1,          
  TCP_SYN_SENT,
  TCP_SYN_RECV,
  TCP_FIN_WAIT1,
  TCP_FIN_WAIT2,
  TCP_TIME_WAIT,
  TCP_CLOSE,
  TCP_CLOSE_WAIT,
  TCP_LAST_ACK,
  TCP_LISTEN, 
  TCP_CLOSING   /* now a valid state */
};
Also, this thread says that you can detect CLOSE_WAIT by reading EOF.  But since you're concerned about whether data has been sent, you'll probably need to unpack up to tcpi_last_data_sent.
Finally, a caveat.  I took on the challenge of answering your question 'cause it sounded fun and it was but my C legs are still wobbly so YMMV. :)