Looking at the Greek use of sleep and dead, Jarius daughter was sleeping as jesus said. The greek word he used always meant sleeping not dead.
koimaō can mean dead or a sleep not used in jarius daughters story.
Mat_27:52; Mat_28:13; Luk_22:45; Joh_11:11; Joh_11:12; Act_7:60; Act_12:6; Act_13:36; 1Co_7:39; 1Co_11:30; 1Co_15:6; 1Co_15:18; 1Co_15:20; 1Co_15:51; 1Th_4:13; 1Th_4:14; 1Th_4:15; 2Pe_3:4.
1.) asleepG2837 koimaō to put to sleep, fall asleep: — asleep (3), dead (1), fallen asleep (7), fell asleep (3), sleep (2), sleeping (2). used for sleeping but usually dead 18 verses
Joh 11:11 ThisG3778 He saidG3004, and afterG3326 that He *saidG3004 to them, "Our R1friendG5384 LazarusG2976 R2has fallenG2837 asleepG2837; but I goG4198, soG2443 that I may awakenG1852 him out of sleepG1852."
Act 7:60 ThenG2532 R1fallingG5087 on his kneesG1119, he criedG2896 out with a loudG3173 voiceG5456, "LordG2962, R2do not holdG2476 thisG3778 sinG266 against them!" Having saidG3004 thisG3778, he N1 R3fellG2837 asleepG2837.
1Co 15:6 AfterG1899 that He appearedG3708 to moreG1883 thanG1883 fiveG4001 hundredG4001 brethrenG80 at oneG2178 timeG2178, mostG4183 of whomG3739 remainG3306 untilG2193 nowG737, but someG5100 R1have fallenG2837 asleepG2837;
1Co 15:18 ThenG686 thoseG3588 alsoG2532 who R1have fallenG2837 asleepG2837 in ChristG5547 have perishedG622.
1Th 4:13 But R1we do not wantG2309 you to be uninformedG50, brethrenG80, aboutG4012 thoseG3588 who R2are asleepG2837, soG2443 that you will not grieveG3076 as do R3the restG3062 who haveG2192 R4noG3361 hopeG1680.
katheudō used in Jarius story
Mat_8:24; Mat_9:24; Mat_13:25; Mat_25:5; Mat_26:40; Mat_26:43; Mat_26:45; Mar_4:27; Mar_4:38; Mar_5:39; Mar_13:36; Mar_14:37; Mar_14:40; Mar_14:41; Luk_8:52; Luk_22:46; Eph_5:14; 1Th_5:6; 1Th_5:7; 1Th_5:10.
asleepG2518 katheudō; (to sleep); to sleep: — asleep (8), do their sleeping (1), goes to bed (1), sleep (3), sleep do (1), sleeper (1), sleeping (8). always used for sleeping all 20 verses
Mar 5:39 And enteringG1525 in, He *saidG3004 to them, "WhyG5101 makeG2350b a commotionG2350b and weepG2799? The childG3813 has not diedG599, but is asleepG2518."
Mat_8:24 And beholdG2400, there aroseG1096 N1a greatG3173 stormG4578 on the seaG2281, soG5620 that the boatG4143 was beingG2572 coveredG2572 with the wavesG2949; but Jesus HimselfG846 was asleepG2518.
Mat_13:25 "But whileG1722 his menG444 were sleepingG2518, his enemyG2190 cameG2064 and sowedG1986b N1taresG2215 amongG303 G3319 the wheatG4621, and wentG565 awayG565.
Mat_26:40 And He *cameG2064 to the disciplesG3101 and *foundG2147 them sleepingG2518, and *saidG3004 to PeterG4074, "SoG3779, you men couldG2480 not R1keepG1127 watchG1127 with Me for oneG1520 hourG5610?