This is the result
# ldd /usr/bin/ldapsearch
linux-vdso.so.1 => (0x00007fff71dff000)
libldap-2.4.so.2 => /usr/lib64/libldap-2.4.so.2 (0x000000303a400000)
liblber-2.4.so.2 => /usr/lib64/liblber-2.4.so.2 (0x000000303ac00000)
libsasl2.so.2 => /usr/lib64/libsasl2.so.2 (0x0000003038000000)
libcrypt.so.1 => /lib64/libcrypt.so.1 (0x0000003033a00000)
libresolv.so.2 => /lib64/libresolv.so.2 (0x0000003023a00000)
libssl3.so => /usr/lib64/libssl3.so (0x0000003036a00000)
libsmime3.so => /usr/lib64/libsmime3.so (0x0000003036e00000)
libnss3.so => /usr/lib64/libnss3.so (0x0000003035200000)
libnssutil3.so => /usr/lib64/libnssutil3.so (0x0000003036200000)
libplds4.so => /lib64/libplds4.so (0x0000003035a00000)
libplc4.so => /lib64/libplc4.so (0x0000003034e00000)
libnspr4.so => /lib64/libnspr4.so (0x0000003035e00000)
libc.so.6 => /lib64/libc.so.6 (0x0000003021a00000)
libdl.so.2 => /lib64/libdl.so.2 (0x0000003022200000)
libfreebl3.so => /lib64/libfreebl3.so (0x0000003033e00000)
libpthread.so.0 => /lib64/libpthread.so.0 (0x0000003022600000)
libz.so.1 => /lib64/libz.so.1 (0x0000003023200000)
/lib64/ld-linux-x86-64.so.2 (0x0000003021200000)
As I see libssl3.so... I would say that openssl is used...