A first approach (which can be justified asymptotically) could be fitting a nonparameteric density estimator (KDE, for example) to your data and then sampling from it. I think it is impossible to sample exactly from the same density, unless it is known.


    #Your data
    x=c(-0.38848247,0.21655804,-1.08211969,0.00369104,0.0993393,0.25531731,
    1.40574444,-1.80271115,-0.58780605,-0.35026458,0.67197532,-1.29654652,
    -0.58874467,-0.4004176,1.46242829,0.83946654,-0.24861179,-1.604154,
    1.53555232,1.45589014,-0.52092604,1.65504054,0.12854317,1.66771236,
    1.47964458,-1.55677722,-0.40070632,-0.41957953,0.37803884,0.45349904,
    1.18265468,1.43979945,-1.55395031,0.01054229,0.48887945,0.12949194,
    -0.40283111,1.2998402,-1.02205575,-0.34370088,0.22117962,0.52840463,
    -0.9584811,1.22482249,-1.51189671,0.372597,1.68446854,-0.74440632,
    1.33920212,0.18072373,-0.35813474,0.39400846,1.18971633,1.02192759,
    -1.90422461,0.18459334,0.18096905,-1.73870267,1.57349896,-1.05632536,
    0.1864611,-1.49696658,0.51070568,-2.25007651,-0.64768552,1.80404194,
    2.25164576,-0.07925576,-0.83550267,-1.65513631,0.25913869,0.36030077,
    -0.09006407,-1.64359237,-0.1312756,-0.13790883,-0.09940115,-0.02089164,
    -0.60924589,-0.05451811,2.11736111,-1.40329353,-0.71788744,-0.45888623,
    -0.75608368,0.45762458,-0.24299548,-0.29224218,-1.0488731,-0.62028903,
    -0.08257067,0.92297771,0.2964071,-0.02598973,-0.20439059,-0.25195469,
    0.20572878,-0.49343988,0.25886695,1.20595313)
    
    # sample size
    length(x)
    
    # KDE
    plot(density(x))
    
    # Sampling from a KDE
    samplekde = function(n,data){
    resp = vector()
    samp = sample(1:length(data),n,rep=T)
    h = density(data)$bw
    for(i in 1:n) resp[i] = rnorm(1,data[i],h)
    return(resp)
    }
    
    # Example
    x1 = samplekde(100,x)
    
    plot(density(x1))
    points(density(x),col="red",type="l")
    
    # qqplot to check how similar x and x1 are
    qqplot(x,x1)


Page 5 of this file

http://www.stat.cmu.edu/~cshalizi/350/lectures/28/lecture-28.pdf

The bandwidth parameter used in my code is the one used by default in the R command `density()`.