I also reproduced this issue on N4, OSK does not come up once BT mouse is connected, no matter BT keyboard is connected or not, the OSK will come up if disconnect the BT mouse, got the below output, fyi.
$ adb shell ./lsinput
/dev/input/event0
bustype : (null)
vendor : 0x0
product : 0x0
version : 0
name : "pmic8xxx_pwrkey"
phys : "pmic8xxx_pwrkey/input0"
bits ev : EV_SYN EV_KEY
/dev/input/event1
bustype : BUS_I2C
vendor : 0x1
product : 0x1
version : 1
name : "keypad_8064"
phys : "keypad_8064/input0"
bits ev : EV_SYN EV_KEY EV_MSC
/dev/input/event2
bustype : (null)
vendor : 0x0
product : 0x0
version : 0
name : "touch_dev"
bits ev : EV_SYN EV_ABS
/dev/input/event3
bustype : (null)
vendor : 0x0
product : 0x0
version : 0
name : "apq8064-tabla-snd-card Button Ja"
phys : "ALSA"
bits ev : EV_SYN EV_KEY
/dev/input/event4
bustype : (null)
vendor : 0x0
product : 0x0
version : 0
name : "apq8064-tabla-snd-card Headset J"
phys : "ALSA"
bits ev : EV_SYN EV_SW
/dev/input/event5
bustype : (null)
vendor : 0x1
product : 0x1
version : 1
name : "hs_detect"
bits ev : EV_SYN EV_KEY EV_SW
I also reproduced this issue on N4, OSK does not come up once BT mouse is connected, no matter BT keyboard is connected or not, the OSK will come up if disconnect the BT mouse, got the below output, fyi.
$ adb shell ./lsinput pwrkey/ input0"
/dev/input/event0
bustype : (null)
vendor : 0x0
product : 0x0
version : 0
name : "pmic8xxx_pwrkey"
phys : "pmic8xxx_
bits ev : EV_SYN EV_KEY
/dev/input/event1 8064/input0"
bustype : BUS_I2C
vendor : 0x1
product : 0x1
version : 1
name : "keypad_8064"
phys : "keypad_
bits ev : EV_SYN EV_KEY EV_MSC
/dev/input/event2
bustype : (null)
vendor : 0x0
product : 0x0
version : 0
name : "touch_dev"
bits ev : EV_SYN EV_ABS
/dev/input/event3 tabla-snd- card Button Ja"
bustype : (null)
vendor : 0x0
product : 0x0
version : 0
name : "apq8064-
phys : "ALSA"
bits ev : EV_SYN EV_KEY
/dev/input/event4 tabla-snd- card Headset J"
bustype : (null)
vendor : 0x0
product : 0x0
version : 0
name : "apq8064-
phys : "ALSA"
bits ev : EV_SYN EV_SW
/dev/input/event5
bustype : (null)
vendor : 0x1
product : 0x1
version : 1
name : "hs_detect"
bits ev : EV_SYN EV_KEY EV_SW
/dev/input/event6
bustype : BUS_BLUETOOTH
vendor : 0x46d
product : 0xb014
version : 4608
name : "Bluetooth Mouse M336/M337/M535"
phys : "e1:d1:70:f7:d6:98"
uniq : "ae:5b:98:20:1f:00"
bits ev : EV_SYN EV_KEY EV_REL EV_ABS EV_MSC EV_LED EV_REP